I don't understand how the two could really be one and the same. E.g. we can exert forces $\vec{F}$ and $-\vec{F}$ on a body and it's acceleration will not change. I don't think it makes sense to say that a body at rest is accelerating equally in all directions. So what does it mean to say that force and mass $\times$ acceleration are equal to each other?
"For example" because I feel that my misunderstanding is more fundamental than just this.
Best Answer
$\vec{F}$ in the $\vec{F}=m\vec{a}$ is the net force acting on the body. In other words, Newton's second law of motion should be written
$$\vec{F}_{net}=m\vec{a}$$
Hope this helps.