The Space Shuttle did something like this, the rocket boosters were landed in the ocean with parachutes and reused. I found a PDF from NASA which describes the procedure. They disassembled the entire thing into parts, inspected each part for damage, and then restored and reused the parts as appropriate. By contrast, I think what SpaceX is aiming for is more like an airplane, you just fill the tank with new fuel and launch it again.
(The PDF claims that the refurbishment program is cost effective, but word of mouth has it that if you factor in the cost of retrieving the boosters, the whole thing cost more than just manufacturing new ones from scratch. See also this thread in the KSP forum.)
You're also talking about fundamentally different kinds of rocket boosters. The Space Shuttle used solid fuel boosters, which are basically nothing except a tube packed full of energetically burning material, an igniter to light said material, and a nozzle for the generated gases to come out. They couldn't throttle, couldn't gimbal, couldn't shut off or restart, didn't use cryogenic fuel so didn't need insulation, didn't rely on pressurized fuel so they didn't need turbopumps... In fact, as far as I know they basically didn't have any moving parts at all!
Y...
This thread is for asking any questions that might seem obvious, tangential, silly or what-have-you. Don't be shy, everyone has holes in their knowledge, though the fewer and the smaller we can make them, the better.
Please be respectful of other people's admitting ignorance and don't mock them for it, as they're doing a noble thing.
To any future monthly posters of SQ threads, please remember to add the "stupid_questions" tag.