It depends on the wiring standard. As far as I know a TRS plug will always* (* for normal audio-wiring standard usage) "work" in a TRRS socket, but of course you only get stereo sounds, no mic/video (since you don't have a mic or video plugged in obviously..). This works because the large ring will always contact both the mic and, more importantly the ground connection, making the needed ground connection. Yes it will short the mic input but I don't think this ever harms anything.
The other way is more complicated. I believe a CTIA (apple standard) TRRS plug will always work in a stereo TRS socket, again, just for stereo. (I'm not a huge apple fan, personally, but it seems to me that in this very important sense, apple is more standard not less as people like to claim). This might not be true for OMTP, and my experience seems to confirm this. The other way may kind of "work" but you're grounding the earbuds through the mic! => much lower volume, terrible sound, probably huge cross talk, may destroy mic. Amusingly I have found that pressing the talk button can make this configuration work in a pinch (think tape) as apparently the talk button shorts the mic line for many android devices at least (I think this is outside of either of the above two mentioned standards). YMMV, just one headset and one observation.
Of course TRRS in a TRRS socket is yet another issue, and for everything to work, it has to use the same wiring standard and the headset has to use the same signaling standard as the device.
I have a laptop that seems to accept anything I throw at it with mic and headphones working. Either I've thrown less at it than I realized, or more likely, it auto-senses.
Of course you can find a ton of information about this from very thorough articles on the subject with pictures and everything with a little google searching, being as there are probably at least several hundred million people in the world with equipment that relates to this issue. It's hardly an obscure discussion board kind of question.
