The difference in end result? "Big" as in you'll look good, but not necessarily be strong (hypertrophy, bodybuilding). "Explosive" as in move weight fast, has many sports applications. "Strong" as in you'll end up looking like a bear but you can move ridiculous amounts of weight (albeit slowly).

Big means that you're training for hypertrophy (muscle growth). You gain as much muscle mass as possible, but don't care where. This results in an imbalance, your big muscles get really big but the smaller ones don't. They become the limiting factor in strength. Also, your endurance then sucks.

Explosive strength and strong is more subtle. You basically have two sorts of muscle fiber: one is for short explosive strength the other more endurance. Different training results in a different mix of these fibers (as does genetics!). It's a case of getting the right kind of fiber in the right muscles for your sporting goal.

There are some fantastic youtube videos from people who are experts (for me it's a hobby), I can recommend Shredded Sports Science for the theory and Athlean-X for a mix of both theory and practice.

Look up fast twitch vs slow twitch muscles.