So the question is "How many numbers between $3$ and $101$ are exactly divisible by $4$?" I found out that the answer is $25$.
When reading this question over, a thought came into my head. What if the question said "are exactly multiples of $4$?"
Can someone explain the difference between the two in context of this problem?
The two wordings are synonymous. "$a$ is a multiple of $b$" means neither more nor less than "$a$ is divisible by $b$".
... in the integers, that is. In general rings, "$a$ is divisible by $b$" will almost always mean that there is some $k$ in the ring such that $a=kb$, whereas "$a$ is a multiple of $b$" can sometimes (but not always; you'd need to research each author's usage to be sure) mean that $a$ is an integer multiple of $b$ -- that is, there exists an integer $n$ such that $a=nb$.