The depth of the flute determines bowl or spindle in most cases.
Here is a link to Thompson Tools
From L to R the first two are bowl gouges with very deep flutes whether U or V.
Third is the Spindle gouge and depth of flute is 50% of diameter.
Fourth is the Detail Spindle gouge and depth of flute is 33% of diameter.
Fifth is the Shallow Detail Spindle and depth of flute is 20% of the diameter.
If you click on each pic it will take you to a better view.
The more shallow the flute the tighter place your can turn into such as a bead.
Bowl grinds can also be a Jamieson, 45/45, and other terms. Typically bowl gouges have the wings swept back more than spindle gouges.
A traditional grind (sometimes called a production) is as you say. The wings are almost straight up like a spindle roughing gouge. I do not use one because I am a chicken . If you can control it the cutting edge is very sheer giving a cleaner cut, if you can't control it the top corner is very close to the wood and a small mistake allows it to dig in creating one heck of a catch.
On either type of grind for bowls many people grind a secondary bevel in order to scoot around the area from the side to the bottom easier.
Most gouges now are made from round stock so if it is bowl or spindle the shaft is the same. Older spindle gouges may be formed from flat steel and should not be used inside a bowl IMHO. Typically I would not use a spindle gouge for bowl turning; the exception would be for detail work such as adding beads or working around the base of a tenon.
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