My Wii has both.
I soldered a modchip when it was released, then later I softmodded it when the modchip wasn't useful anymore.
I didn't unsolder it, it's just there, unused. so, it has both.
the hardmod is mostly use to play burned discs or other region, and the softmod to play iso from an external storage.
of course, some softmod could play burned disc too, it would be easy to check such mod without opening the console. It would be harder to check if you have a hardmod without opening the console as it requires removing all softmod and see if burned discs or other region still work.
First, to see if it's softmoded ... it has HBC so it is.
Then, if you want to know which other soft modification you have, you can run syscheck (see the tutorial in my signature) and post the result here.