The reason the quotients in your test case are not equal is that in the math.floor(a/b) case, the result is calculated with floating point arithmetic (IEEE-754 64-bit), which means there is a maximum precision. The quotient you have there is larger than the 253 limit above which floating point is no longer accurate up to the unit.
With the integer division however, Python uses its unlimited integer range, and so that result is correct.
See also “Semantics of True Division” in PEP 238:
Note that for int and long arguments, true division may lose information; this is in the nature of true division (as long as rationals are not in the language). Algorithms that consciously use longs should consider using
//, as true division of longs retains no more than 53 bits of precision (on most platforms).