I've been looking at some wearable camera mounts, and I get the impression that GoPro mounts are different from the standard tripod mount point.
Can I use my video camera with its standard screw-in tripod mount with a GoPro mount?
GoPro cameras do not have a built in tripod mount(1/4-20). They actually have a more specialized quick release clip built into the waterproof housing. To attach a GoPro unit to a tripod mount, you need the GoPro Tripod Mount which runs about $8 these days.
To answer your question, if you want to mount a GoPro camera to a tripod, you need the Tripod mount accessory. The various other mounts that you can get will allow you to mount the GoPro to things like a flat surface, curved surface, pivot arm, or a leather leash. You can pick these up in its "grab bag" mount kit as shown here. Note - this does not come with the tripod mount.
If you are asking about a video camera in addition to the GoPro, that will not work with any of the GoPro mount accessories, because it will not have the quick release GoPro mount.
Here is an image of the GoPro standard housing with built in quick release clip and currently attached to the flat adhesive mount:
This is an image of the GoPro standard housing with the Tripod Adapter mounted to a tripod:
Finally a closeup view of the tripod adapter:
For attaching a regular camera onto a GoPro mount, you can get an adapter. ie something that screws onto the 1/4" tripod mount, and provides a GoPro style "two-prong" attachment.
These should work with any action camera that has a standard 1/4" tripod screw, including the Sony action cameras. Or you could use it with a regular compact camera - but it depends on the strength of the mounts and adapters, they may not be strong enough for a much heavier camera.