They are both just thinned oil varnish mixes
True oil uses Stoddard (Another name for simple "Spirits" )
Birchwood casy used Naptha as the thinner.
They both have oil .. Birchwood Casey has Tung (though I would doubt its true Tung)
True oil "Oils" is proprietary,but probably. a mix of boiled linseed and tung.
These are just copies of Sam Maloofs famous oil varnish mix he used on his stunning furniture...
Formby's "Tung oil" Finish has little to no tung oil in it,, It too is a basic oil varnish mix..
Minwax's "Antique Oil Finish" is another oil varnish mix.. as is Howards "Restore a Finish" but it offers "colored" blends too,"
You can mix your own
1/3 Varnish of your choice (I like Minwax fast dry Polyurethane - semi gloss)
1/3 thinner (Naptha, mineral spirits, paint thinner)
1/3 Oil (boiled lindseen.Tung, or soy.)
I have found thinning it thinner with more solvent (just a bit more) makes it easier to work with.
I just wipe on a liberal coat, with Scotts "Blue" shop towels,, wait till it just gets slightlly tacky,, then wipe off ALL residue. (Tape off Checkering)
The finish is "IN" the wood instead of "On TOP"
Repeat till you get the sheen and build you desire..
The beauty of it is, is you wipe off the residue,,so there is no chance of airborn dust settling on it as it dries..It dries fast, allowing mulitiple coats relativly fast..
Its fool proof! You cant screw it up..
Just make sure the Varnish you choose forr the mix is Oil Based,,not water..
I will say though,, I think its comical people fool around stickin their fingers in it to apply!:) all that does is get your fingers sticky!

But, it is romantic to claim it was hand rubbed!

Easiest finish out there to use..
Its been around for a long time.. and copied often..