Is there a difference between naafil, sunnah, mandoob and mustahabb?

Sunnah
mu’akkadah (confirmed Sunnah), naafil (supererogatory), voluntary and
mandoob (recommended) all share a similar meaning; they are acts of worship
that are enjoined and encouraged in Islam, without being obligatory. The one
who does them will be rewarded but there is no sin on the one who does not
do them. 

That is like
praying qiyaam al-layl (optional prayers at night), the sunan rawaatib
(regular Sunnah prayers), starting on the right when putting on one’s
clothes, and so on. Some of the scholars think that these words are similar
in meaning, whilst others – like the Maalikis – differentiate between them.
In their view “Sunnah” refers to something that the Prophet (blessings and
peace of Allah be upon him) did persistently; naafil refers to things that
he did sometimes and not at other times. 

Ad-Dasooqi
al-Maaliki said: Naafil refers in linguistic terms to something extra or
additional; in Islamic terminology it refers to that which the Prophet
(blessings and peace of Allah be upon him) did but did not do persistently,
i.e., sometimes he did not do it and sometimes he did do it. It does not
mean that he stopped doing it altogether, because one of his characteristics
is that if he did a righteous deed he would not stop doing it altogether
after that. … With regard to “Sunnah”, in linguistic terms it refers to a
way or path; in Islamic terminology it refers to that which the Prophet
(blessings and peace of Allah be upon him) did openly when he was among a
group of people, and he persisted in doing it, but there is no proof to
indicate that it is obligatory. Sunnahs that are described as mu’akkadah
(confirmed) are those that bring a great deal of reward, such as Witr.

End quote from
Haashiyat ad-Dasooqi, 1/312 

Al-Khateeb
ash-Sharbeeni ash-Shaafa‘i said: Chapter on offering naafil prayers. Naafil
in linguistic terms refers to something extra; in Islamic terminology it
refers to actions other than those which are obligatory. They are so called
because they are extra to what Allah, may He be exalted, has made
obligatory. Naafil is similar to Sunnah, mandoob (recommended), mustahabb
(encouraged) and so on. This is the well-known view.

End quote from
Mughni al-Muhtaaj, 1/449 

Ibn an-Najjaar
al-Hanbali said: That which is mandoob (recommended) is called Sunnah,
mustahabb, naafil, and so on… The highest of that which is recommended is
Sunnah, then fadeelah (virtue), then naafilah.

End quote from
Sharh al-Kawkab al-Muneer, p. 126 

It should be
noted that the Hanafis regard the one who does not do Sunnah mu’akkadah
(confirmed Sunnah) actions as having sinned, but they say that his sin is
less serious than that of one who fails to do obligatory (waajib) actions. 

There is no
difference of opinion among the scholars concerning the fact that some
Sunnah actions are more confirmed and bring greater reward than others. Thus
it may seem that this difference of opinion is the matter of a difference in
names only; with regard to the meaning, there is no difference of opinion
concerning it. 

Ibn Nujaym
al-Hanafi said: What appears to be the case from the words of our fellow
scholars in our madhhab is that sin is incurred by failing to do obligatory
(waajib) or sunnah mu’akkadah actions, according to the correct view,
because they clearly stated that the one who omits the sunnahs of the five
daily prayers is not said to have sinned, but the correct view is that he is
sinning. This was stated in Fath al-Qadeer. And they clearly stated
that the one who fails to pray in congregation is sinning even though it is
a sunnah mu’akkadah according to the correct view. And there are other
similar examples to be seen by the one who studies their words. Undoubtedly
the sin in some cases is greater than in others, and the sin of one who does
not do the sunnah mu’akkadah action is less serious than that of the one who
does not do the obligatory (waajib) action. 

End quote from
al-Bahr ar-Raa’iq, 1/319 

And Allah
knows best.