The difference between sending salaams on the Prophet (peace and blessings of Allaah be upon him) and sending blessings

It is prescribed for the Muslim to pray for peace for the
Prophet (peace and blessings of Allaah be upon him) and to send salaams
upon him, just as it is prescribed to pray for blessings for him. The
evidence that it is prescribed to send salaams upon the Prophet (peace
and blessings of Allaah be upon him) is the verse in which Allaah says
(interpretation of the meaning): 

“Allaah sends His Salaah (Graces, Honours, Blessings,
Mercy) on the Prophet (Muhammad), and also His angels (ask Allaah to bless
and forgive him). O you who believe! Send your Salaah on (ask Allaah to
bless) him (Muhammad), and (you should) greet (salute) him with the Islamic
way of greeting (salutation, i.e. As‑Salaamu ‘Alaykum)”

[al-Ahzaab 33:56]

It was narrated that ‘Abd-Allaah said: the Messenger of
Allaah (peace and blessings of Allaah be upon him) said: “Allaah has
angels who travel about the earth, conveying to me the salaams of my ummah.”
(Saheeh Sunan al-Nasaa’i, 1215; al-Silsilat al-Saheehah,
2853). 

It was narrated that ‘Abd-Allaah said: “When we prayed with
the Prophet (peace and blessings of Allaah be upon him) we used to say,
‘Peace be upon Allaah from His slaves and peace be upon So and so.’ The
Prophet (peace and blessings of Allaah be upon him) said, ‘Do not say
“Peace (salaam) be upon Allaah”, for Allaah Himself is al-Salaam. Rather
say, “Al-tahiyyaatu Lillaahi wa’l-salawaatu wa’l-tayyibaat. Al-salaamu
‘alayka ayyuha’l-Nabiyyu wa rahmat Allaahi wa barakaatuhu. Al-salaamu
‘alayna wa ‘ala ibaad-illaah il-saaliheen (All compliments, prayers and
pure words are due to Allaah. Peace be upon you, O Prophet, and the mercy of
Allaah and His blessings. Peace be on us, and on the righteous slaves of
Allaah).” If you say this it will be for all the slaves in heaven and
between the heavens and the earth. [Then go on to say] “Ash-hadu an laa
ilaaha ill-Allaah wa ash-hadu anna Muhammadan ‘abduhu wa rasooluhu (I
bear witness that there is no god except Allaah and I bear witness that
Muhammad is His slave and Messenger).” Then choose whichever du’aa’ you like
and recite it.’”

(Narrated by al-Bukhaari, 835) 

It was narrated that Faatimah, the daughter of the Messenger
of Allaah (peace and blessings of Allaah be upon him) said: “When the
Messenger of Allaah (peace and blessings of Allaah be upon him) entered
the mosque, he would say, ‘Bismillaah wa’l-salaam ‘ala Rasool-illaah.
Allaahumma ighfir li dhunoobi waftah li abwaab rahmatika (In the name of
Allaah, and peace be upon the Messenger of Allaah. O Allaah, forgive me my
sins and open to me the gates of Your Mercy).’ And when he exited he would
say, Bismillaah wa’l-salaam ‘ala Rasool-illaah. Allaahumma ighfir li
dhunoobi waftah li abwaab fadlika (In the name of Allaah, and peace be
upon the Messenger of Allaah. O Allaah, forgive me my sins and open to me
the gates of Your Bounty).’”

(Saheeh Sunan Ibn Maajah, 625) 

It was narrated from Abu
Hurayrah that the Messenger of Allaah (peace and blessings of Allaah be
upon him) said: “There is no one who sends salaams upon me, but Allaah will
restore to me my soul so that I may return his salaams.”

(Saheeh Sunan Abi Dawood, 1795) 

It was narrated from ‘Abd-Allaah ibn Abi Talhah from his
father that the Messenger of Allaah (peace and blessings of Allaah be
upon him) came one day with evident signs of happiness on his face, and he
said: “Jibreel (peace and blessings of Allaah be upon him) came to me
and said, ‘Would it not please you, O Muhammad, to know that no one among
your ummah will send blessings upon you but I will send ten blessings upon
him, and no one among your ummah will send salaams upon you but I will send
ten salaams upon him.”

(Saheeh Sunan al-Nasaa’i, 1228) 

Sending salaams upon the
Prophet (peace and blessings of Allaah be upon him) is one of the
rights that the Prophet (peace and blessings of Allaah be upon him) has
over his ummah. The Muslim is commanded to do this either in general word or
in the specific phrases narrated in the reports, such as sending salaam on
him in the Tashahhud, and when entering or leaving the mosque. The command
to send salaams upon him (peace and blessings of Allaah be upon him)
even in his absence is one of the unique blessings that Allaah has bestowed
upon him alone, which he does not share with anyone else, for it is not
prescribed to send salaams upon any specific person in his absence apart
from him (peace and blessings of Allaah be upon him). Another of his
unique privileges is that the salaams of his ummah are conveyed to him, so a
person may attain the virtue of sending salaams upon the Prophet (peace
and blessings of Allaah be upon him) and it reaching him even if he did not
have the opportunity to meet him during his lifetime and even if a person is
not able to go to his grave after he died. 

With regard to praying for blessing for the Prophet
(peace and blessings of Allaah be upon him), this is also prescribed in
Islam. One of the reports that prove that it is prescribed is the saheeh
report from Abu Mas’ood al_Ansaari who said: “The Messenger of Allaah
(peace and blessings of Allaah be upon him) came to us when we were sitting
with Sa’d ibn ‘Ubaadah, and Basheer ibn Sa’d said to him: ‘Allaah has
commanded us to send blessings upon you, O Messenger of Allaah. How should
we send blessings upon you?’ The Messenger of Allaah (peace and
blessings of Allaah be upon him) remained silent until we wished that he had
not asked him. Then the Messenger of Allaah (peace and blessings of
Allaah be upon him) said: “Say: Allaahumma salli ‘ala Muhammad wa ‘ala
aali Muhammad kamaa salayta ‘ala aali Ibraaheem. Wa baarik ‘ala Muhammad wa
‘ala aali Muhammad kama baarakta ‘ala aali Ibraaheem fi’l-‘aalameen innaka
hameedun majeed (O Allaah, send blessings upon Muhammad and upon the
family of Muhammad, as You sent blessings upon the family of Ibraaheem, and
bless Muhammad and the family of Muhammad, as You blessed the family of
Ibraheem among the nations. Verily You are Most Praiseworthy, Full of
Glory). And the salaam is as you know.”

(Narrated by Muslim, 405) 

Sending salaams upon the Prophet (peace and blessings of
Allaah be upon him) may be done by saying “Al-salaamu ‘alayka
ayyuha’l-Nabiyyu wa rahmat Allaahi wa barakaatuhu (peace be upon you, O
Prophet, and the mercy of Allaah and His blessings). Or it may take the form
of a du’aa’, praying that Allaah may keep him sound, such as saying Sall
Allaahu ‘alayhi wa sallam (may Allaah send blessings and peace upon him
[i.e., the Prophet (peace and blessings of Allaah be upon him)]. A
person’s sending salaam upon the Prophet may be done by mentioning Allaah’s
name al-Salaam by way of seeking the blessing of that name and this name is
suited to the context because you are asking Allaah to keep him safe and
sound, as if one is saying “O Allaah, Whose name is al-Salaam, keep your
Prophet (peace and blessings of Allaah be upon him) safe and sound.”
When the word Salaam refers to the name of Allaah, it appears with
the definite article al-, unlike when the word salaam appears
in the context of praying for peace, tranquility and soundness to be
bestowed by Allaah upon His slaves, in which case it appears without the
definite article. “Because salaam from Him means any amount of salaam, and
any amount of salaam from Him will be sufficient to make any slave of Allaah
have no need of salaam from anyone else and no need for any greeting from
anyone else; and any salaam from Allaah will be sufficient to grant him all
of his wishes. So the least salaam from Allaah – and nothing can be
described as least when it comes from Allaah – will bring the greatest
blessings and will ward off all causes of misery, and will make life good
and will ward off all causes of doom and destruction. Therefore in this
context, when speaking of salaam from Allaah, there is no need for the
definite article.”

See Dabaa’i’ al-Fawaa’id, 2/143 

What is meant by salaam is being free from evil and faults.
So the one who sends salaams upon the Prophet is praying for him (peace
and blessings of Allaah be upon him) in this sense, asking for the Prophet
(peace and blessings of Allaah be upon him) to be protecte from evil,
faults and shortcomings. As for blessings (barakah), what this means is
steadfastness and stability. Blessing means growth and increase.

 What is meant by praying for blessing for the Prophet
(peace and blessings of Allaah be upon him) is asking Allaah to bestow good
upon him, to make it lasting, to increase and multiply it.

 And Allaah knows best.