It's an old garage with a wooden door on it currently.
Question is, I measured the size of the actual wooden door itself and
it comes out to 94" (7' 8") width and 78" (6' 5") in height.. I see listed
is a standard size of 8' x 7'. When they quote these sizes, are they
quoting what it will be with the hardware or the door itself?

Thats the size of the door itself. Standard "roll up" doors don't fit
INSIDE the opening, they go on the inside of the garage, AGAINST the
opening, therefore there would be a 2" overlap on either SIDE of your
opening and about 6" ABOVE your opening. A narrow piece of weatherstrip all
around seals the edges against weather. The hardware holds in it place.
This is a simple job for an installer as long as you have the overhead and
side clearance inside the garage.

Go look at a neighbors 'overhead' door and see how they work.