Well, there is video editing and special effects. The two are seperate things and typically will come in seperate packages.

You are familiar with Photoshop so you might favour the Adobe offerings. Premiere pro or premiere Elements is their video editor. But for special effects or 'combining movies' (more commonly referred to as 'composritting' in the editting circles) you will want to have a look at After Effects.

These are not the only options available to you. They are hardly the cheapest and a substancial learning curve may be ahead of you (more so with After Effects).

I quote Adobe s/w because it's what I know. Other, I'm sure will have recommendations for s/w they are familiar with.

__________________
I'm not young enough to know everything!