If people pretend to know medicine and prescribe remedies, but they are not doctors, and they cause the death of a sick person, is the ruling the same as that on one who killed deliberately?

Firstly: 

Allah, may He be exalted, says (interpretation of the meaning):

“Because of
that We ordained for the Children of Israel that if anyone killed a person
not in retaliation of murder, or (and) to spread mischief in the land – it
would be as if he killed all mankind, and if anyone saved a life, it would
be as if he saved the life of all mankind”

[al-Maa’idah 5:32]. 

What is meant is killing a soul that Allah has made it forbidden to kill.
Sa‘eed ibn Jubayr said concerning the words “it
would be as if he killed all mankind”:
Whoever regards it is permissible to shed the blood of a Muslim, it is as if
he regards it is permissible to shed the blood of all people, and whoever
regards it as forbidden to shed the blood of a Muslim, it is as if he
regarded it as forbidden to shed the blood of all people. 

Mujaahid said: Whoever kills a believing soul deliberately, Allah will make
his recompense Hell, and Allah will be angry with him and will curse him,
and will prepare for him a severe punishment. He is saying that if he killed
all the people, that would not increase such a punishment. 

Tafseer Ibn Katheer
(3/93) 

As-Sa‘di (may Allah have mercy on him) said: That is because he had no
legitimate reason to do so, and no one should kill another person unless he
has a legitimate reason to do so. If a person has the audacity to kill
someone who did not deserve to be killed, it means that he does not
differentiate between the one whom he killed and anyone else; rather he
would do that every time his soul that is inclined towards evil prompts him
to do so. Therefore his audacity in killing him is as if he killed all of
mankind. 

End quote from Tafseer as-Sa‘di (p. 229). See also: al-Jawaab al-Kaafi
by Ibn al-Qayyim (p. 103) 

With regard to the verse in which Allah, may He be exalted, says
(interpretation of the meaning: “The
recompense of those who wage war against Allah and His Messenger and do
mischief in the land is only that they shall be killed or crucified or their
hands and their feet be cut off on the opposite sides, or be exiled from the
land” [al-Maa’idah 5:33],

Even though what these ignorant people and others like them do of spreading
mischief on earth – and in fact all acts of sin and disobedience towards
Allah –  comes under the heading of spreading mischief on earth and
corrupting it, this verse has a different meaning and refers to a different
ruling that does not have to do with the topic of this question, because
those referred to in this verse are those who want to spread mischief
deliberately and intentionally, and they strive to do that on earth so as to
spoil it, ruin it, destroy crops and livestock, and terrorise people who
feel secure. 

Moreover, this verse is speaking of a specific group of evildoers and
mischief-makers on earth. Not everyone who spreads mischief on earth
deliberately or transgresses against others comes under the ruling referred
to in this verse. 

Shaykh as-Sa‘di (may Allah have mercy on him) said:

Those who wage war against Allah and His Messenger are those who show enmity
to them openly and spread mischief on earth by promoting disbelief, killing,
seizing wealth and engaging in banditry. 

The well-known view is that this verse has to do with rulings on bandits who
attack people in the cities and in the wilderness or countryside, taking
their wealth by force, killing them and terrorising them, so that people
refuse to travel by the roads where they are, thus cutting off those
routes. 

Allah tells us that their recompense and punishment, when the hadd
punishment is carried out on them, is that one of the things mentioned
should be done to them. 

End quote from Tafseer as-Sa‘di (p. 229) 

Secondly: 

With regard to what you mentioned about this person taking it upon himself
to prescribe herbal medicines and remedies for diseases, if he does not have
experience in what he is doing, and is not known to have knowledge in that
field – if, as a result of his ignorance, he causes the death of an
individual, then he must pay the diyah (blood money) because of the offence
that he committed against another person as a result of his ignorance and
transgression, but despite that he is not regarded as one who killed
deliberately, as the verse mentions, and qisaas (legal retribution) is not
stipulated in that case. 

Al-Khattaabi (may Allah have mercy on him) said: 

I
do not know of any difference of opinion concerning the fact that if a
healer oversteps the mark and the patient dies, he is liable, and the one
who engages in a field of which he has no knowledge is regarded as having
overstepped the mark. If his deed results in death of the patient, then he
is liable for the diyah (blood money), but the qisaas (legal retribution) is
waived in his case, because he did not do that without the permission of the
patient.

End quote from Ma‘aalim as-Sunan (4/39) 

For more information, please see also the answers to questions no.
114047 and 129551. 

And Allah knows best.