I use 1/4 drill bit for a 5/16 lag screw in most materials.

It's a screw that cuts its own threads, as opposed to a bolt requiring a bolt-hole to be tapped (a process that pre-cuts the threads). Lag screws are used in bone surgery where the screw anchors into the bone itself. This saves a multi-step procedure that a regular bolt would require, with no real downside.

I've heard of clutch screw, refers to the type of head, like straight or phillips. Possible carriage bolt, a flat or slightly rounded head bolt with a square shank under the head. A coach screw is a large screw with a hex head.

Searching on the internet I find that "Lag bolts" are sometimes called "coach screws". We think that a "coach screw" is a lag bolt on one end and machine treads on the other, uses would be like attaching a bathroom sink to wood stud walls.

The sink sits on the pedestal and there is a hole or slot on the bottom edge that rests against the wall. A large screw or lag screw is put through these holes and into the wall. There should be a 2x6 or wider board in the wall for this purpose in the original construction.

3/16 inch since you are using a screw and you want the threads to catch the wood

if you meant lag bolt, make it 5/16 inch so the bolt will slide through