Joe,there are both software and hardware synths.

I've not bought a sound card in years but can use the sound cards built into PC motherboards. There is nothing built in to any of the computers here that could play MIDI and my guess is that it would be unusual to find something on that line that did.

My desktop is connected via an old Edirol UM 2 to a Yamaha keyboard and that "just works" with Linux.

The other alternative I have it to install a software synth. FluidSynth is one but I use Timidity. Setting this up on OpenSuse (some other Linux may be a bit more friendly) was still a bit messy last time I looked as you need to find a SoundFont (Merlin Gold is a possibility) to get from something like just piano and drum to a range of instruments and passible sound and some file to map the instruments. It can be done and is done but it's not something I'd think every user would want to do.