Standard base molding works just fine. Prime all sides first if it isn’t already. It’s applied to the drywall portion only. Not the concrete.

The drywall cannot come down close to the garage floor. It will disintegrate when you are spraying for cleaning.

What moulding should I use for the second half that's more L-shaped, to cover the exposed boards?

None. It’s a garage, not your living room.

But I want to cover the exposed boards.

I would use a sealing paint like Zinsser. They make some SERIOUS sealing/primer.

The question becomes, how did this wood get exposed in the first place?

The notch is a transition from outside garage wall to house wall, pretty typical to make the walls match up where it matters most. The exposed wood plate is pressure treated for concrete contact, the plywood is subfloor and nothing wrong with it being exposed in a garage, but not what I would do. Likely this was built per plan. When one wants a garage finished at a higher level, it takes more work and if it gets covered with garage cabinets it is a bit of a waste but I've done it.

1. You could fir out the walls to match - wood strips, more drywall

2. cover the existing wood with more drywall, but it would create a ledge

Use rubber base at the floor. It can also go from wall to top of stem walls where that condition is. Epoxy the stem walls where exposed to make it more consistent.

What moulding should I use for the second half that's more L-shaped, to cover the exposed boards?

Measure from the floor to the top of the exposed wood and cut a piece of 1/2" thick wood/plywood to bring that surface out flush with the sheetrock. Then install baseboard molding all along that wall. If you want to hide that funny little strip of sheetrock above the ledge, cut a piece of wood or baseboard molding maybe 1-1/2" high and nail it in place. Paint everything if you want it to look a bit better. It won't be featured in House Beautiful, but it will be adequate for a garage.