A freewheel screws onto a FREEWHEEL HUB
A coaster brake is integrated INTO a coaster hub.
Because of the size and configuration of a coaster hub, there are some coaster to freewheel adapaters that allow you to screw a freewheel onto a coaster hub... But, not the other way around.
If you want a coaster brake, you have to purchase a coaster hub, which is very tough to find in a good 36 or 48 hole variety, then build it into your existing wheel and depending on the size of the flanges on the coaster hub, you may need new spokes as well.
So, I suppose I can just get a 16" wheel/tire combo and switch it up for the time being?
Seriously, is there any reason I couldn't/wouldn't want to do that?
Would this stuff be interchangable between different brand bikes?
You can buy a cheap, POS bike from Goodwill for 20 bucks with 20" wheels and a coaster brake. Just don't ride it in any shape or form in a harsh manner.
I got one of my Japanese Suntour shells (top notch coaster) from a Barbie 12 inch bike. Welded 48 hole flanges on and rode it for several years. Parts most definitely are interchangable as long as measurements are correct... They usually are.