The very next verse commands people not to assume anything about someone who claims Islam except that he is a believer:
O you who have believed, when you go forth [to fight] in the cause of Allah, investigate; and do not say to one who gives you [a greeting of] peace "You are not a believer," aspiring for the goods of worldly life; for with Allah are many acquisitions. You [yourselves] were like that before; then Allah conferred His favor upon you, so investigate. Indeed Allah is ever, with what you do, Acquainted. (4:94)
So, it is clear there is no distinction in murder between Muslims and believers when we are not allowed to make such a distinction in the first place. Allah explicitly commands us to assume people are believers.
The above verse 3:94 was revealed in the following context:
Ibn 'Abbas said, "A man
from Bani Sulaym, who was tending a flock of sheep, passed by some of
the Companions of the Prophet and said Salam to them. They said (to
each other), 'He only said Salam to protect himself from us.' Then
they attacked him and killed him. They brought his sheep to the
Prophet, and this Ayah was revealed." (Musnad Ahmad)
Plenty of other similar incidents are narrated:
Usama ibn Zaid narrated: God’s Messenger sent us to some people of Juhaina, and I attacked one of them and was about to spear him when he said, “There is no god but God.” I then speared him and killed him, after which I went and told the Prophet. He said, “Did you kill him when he had testified that there is no god but God?” I replied, “Messenger of God, he did that only as a means to escape death.” He asked, “Did you split his heart (to see his true motives)??”* (Sahih Bukhari and Muslim)
The reason Allah would use the label "believer" in this verse when forbidding murder rather than Muslim is to emphasize the gravity of killing them. When you forbid something, you would use the highest words applicable so that it shows people how evil the deed is.
A general rule is that the distinction of Iman and Islam is something only Allah can decide, and it is not for humans to determine. We are to assume Muslims are believers.
The usage of Iman in the Quran and Sunnah is not simple, and it requires its own question and topic.
But, to put it simply, it is not uniform such that one can always assume Iman is a higher level than Islam.
There are several times Iman is considered more than Islam, several times they are used synonymously, and several times Iman is considered less than Islam.