As mentioned, there are two primary factors for a given TOF (time of flight): MV and BC (muzzle velocity and ballistic coefficient of drag), and the interplay of the two, cumulatively, with each passing millisecond (since, as a bullet slows, its vel at that moment in time changes, which can slightly affect the BC itself, and since the worse the BC, the faster it slows, and this effect is exacerbated the higher the initial velocity; therefore, the longer a "low BC" bullet is in flight, the less proportional negative effect the poor BC has on it, because it slows down, lessening the effect of air on it).
However, note that this excludes angle of shot (i.e. it assumes a perfectly horizontal barrel). So I suppose you could say that "angle" is one of the components - it is really, but I think you're asking "excluding angle".
And note that BC of a bullet can change with velocity itself - whereas bullet A might have a slightly better BC than bullet B in the "midrange" of velocity (1800-2400 fps), bullet B might have a slightly better BC than bullet A in the "high" (over 2400) or "low" general-velocity ranges.
And yes, ALL of this is how we describe the effect of gravity on an object moving horizontally (initially) in the air.
Also, note that there are some other factors: Air density, which is a function of elevation, bullet spin rate (spin can actually cause the bullet to rise or fall), and possibly others (I don't *think* ambient temp. makes any difference in and of itself; rather, only as a it applies to affecting MV due to increased pressure).
Also note that there are many various factors which in turn determine the two key factors of MV and BC. MV is affected by powder charge, pressure, barrel length, chamber and barrel temp, powder temp (and ambient temp), bullet weight, rifling type, barrel slickness, bullet slickness (coatings, material), bore diameter vis a vis bullet diameter, bullet bearing surface area, etc. BC is affected primarily by bullet shape (which in turn has many components - length to width ratio and others), and to a lesser extent raw weight.
Excluding TOF (which is of course the main factor - giving gravity time to work on the projectile) - in other words, assuming equal time of flight, the factors which affect the fall rate (and total fall, or total drop) the most, in order are:
1. MV (except that at looooong ranges, BC surpasses MV in overall importance; i.e. #1 and #2 here can switch places)
2. BC
3. Rise (or fall) due to bullet spin (think pitcher's curve ball)
4. Air density due to elevation (nitrogen, oxygen, etc. density)
I may have 3 and 4 backwards, but that's relative - a HUGE change in elevation could trump a small change in bullet spin rate; whereas a huge change in bullet spin rate (and thus rise or fall) could trump a small change in elevation.
There may be others I'm forgetting or don't know (Coriolis effect?, etc.) I suppose if you shoot directly AGAINST the spin of the earth, the time before hitting the ground would be shorter than if you shot directly with the spin of the earth, ceteris paribus, no?
Wind is another one, which would normally be excluded from this "drop" conversation / calculation. But direct and strong downdrafts or updrafts, though fairly rare, could obviously affect bullet drop, as could heavy rainfall.
But yes, even the gravity "rate" or level could make a tiny tiny tiny difference. This could depend on whether the moon is directly overhead or directly on the opposite side of the earth (or not), as well as where on the earth you are (gravity is slightly less at the equator, where the earth is "fatter"). But these differences are infinitesimally small, in reality.