SSD = solid state drive? If so, flash memory is pretty well immune to normal magnets. Even smashing it with the hammer is more likely to break the circuit board or break the leads off the chips, both of which are possible to recover from if you have the time and money to remove the die from the packaging. Even if you break the chip you might not break the die apart.
The screwdriver and hammer comment might be something as simple as removing the HD from the computer, opening up the drive to access the platters and then smashing those. That's how I usually destroy hard drives when I recycle a computer.
Solid State Disks rely on a number of parameters to function properly. Each chip works in concert with the rest to provide contiguous storage. If you break or magnetically interfere with a single chip, you interrupt the storage circuit and data loss occurs. With a large enough magnet or EMP generated from simple static electricity, you could easily destroy a SSD.
As far as spinning disk, you are correct. Destroy the platters, you destroy the storage. If platters are intact, even if they’re scratched, SOME data can be recovered.