I've read that statement many many times on the all knowing Net. The best I can trace it back to is an article in Fine Woodworking some years ago,,I forget the authors name. He was specificly refering to Homer Formby products and their Tung Oil Finish,,stating that the stuff contained no tung oil at all.
He never put forth any proof or spec info, just his statement, But that statement has really stuck.

True, the stuff is not 100% tung oil, it's at least 60% mineral spirits. It places it in a catagory commonly known as 'wiping varnishes' which is what it's sold as.
Wether that's an o'fficial professional wood finishers term or not I don't know but it's a good descriptive one. Several products from different mfg'rs are the same mix & make up.
Wether the base oil is linseed, tung, or another veg based oil,,use one that gets the results you like.

Long, short or medium oil varnishes can be had in any oil varnish. That term only describes the % of oil vs the vehicle. The higher the oil content to the vehicle (min spirits generally, though turp can be used and there are lots of synthetic mixes), the longer it takes to dry.
The advantage in most cases to a 'long oil varnish' is a more flexible finish that won't crack and craze, but type of oil base used and the drying conditions, wood moisture content ect all figure in. They are slower drying as the oil content increases.

Way too much for the average hobby person wanting to finish a set of grips most times. So the simple from the bottle Linspeed, Tru-Oil, or wiping varnish type finishes (wether they are Linseed, Tung or other oil based) are about the easiest to use.

I like the Tung oil varnish, drys fast(er) and hard than linseed oil based varnishes for me at least. I sand in the first couple coats to fill the grain but first heavily stain the wood w/ alcohol stain.
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The sanding fills the grain and will lighten the staining some resulting in the silk smooth surface I'm after. Then you can build up a finish on top as deep as you want or leave it looking like a hand rubbed in oil finish without any build up by applying the thinnest of coating.
A final rubdown w/rottenstone cuts the glare,, and there you are.
Set it in the corner and let it cure for a week or 2 after the final rubdown. Go do something else and just let it set.