According to the Mesilas Yesharim (beginning of ch. 24), there are 2 major divisions of yir'ah, of which one is subdivided.
1- Yir’as ha’onesh: fear of punishment. This is the lowest of the three. However, since even fear of punishment is a motivator, even yir’as ha’onesh is viewed positively.
R’ Shlomo Wolbe zt”l writes that today, we’ve lost that motivating quality. Punishment invokes more thoughts of rebellion than of compliance. He therefore bans corporal punishment of children, and also plays down the role of yir’as ha’onesh a generation raised on democracy, rights, and personal freedoms.
2- Yir’as Shamayim: fear of [the One in] heaven
This is the lofty goal. It, in turn, comes in two flavors:
2a- Yir’as hacheit: fear of sin. This is distinct from the fear of punishment; it’s fear of the sin itself, of the possibility of erring. Mesilas Yesharim continues that when a traditional source speaks of “yir’ah” without specification, it means yir’as hacheit (fear of the sin [itself]).
2b- Yir’as haRomemus: fear of the Grandeur [of G-d]
Note that as the Ramchal progresses, the translation for yir’ah as “fear” becomes steadily less compelling, and that of awe, or acting with awareness of the magnitude of what one is engaging in, seem more appropriate.
The Ramchal writes that the default meaning of yir'as Shamayim is yir'as hacheit. The name of the middah in the beraisa he bases Mesilas Yesharim on is "yir'as hachait" and that is reflected in the names of the relevant chapters.
To explain how fear of sin and awe of Divine grandeur are aspects of the same thing, the Ramchal writes (adapted from R' S Simmons zt"l's translation):
It consists in a person's constantly
fearing and worrying that some trace of sin might have intruded itself into his actions or that they
contain something, small or great, which is inconsonant with the grandeur of HQBH's
honor and with the majesty of His Name. Here we see the strong relationship between yir'as hacheit
and fear of yir'as haromemus - their common concern being that one do nothing in opposition to the
great Majesty of HQBH.
So it would seem that by definition, someone cannot both reject halakhah and have yir'as Shamayim. But that's rejection, a rebellious turn away from what they would accept as G-d's Will if they were being intellectually honest with themselves.
On the other hand, why couldn't someone who was raised or honestly erred and was misled into having a different value system still fear that some action is out of consonance with Hashem's Will, while not sharing Orthodox beliefs about what that will for us contains? They may have the application of the middah misplaced, but that's a matter of knowledge, not middos.