True turpentine is not petrol-based - it was originally distilled from the bark of the terebinth tree. In recent times (especially the junk that's sold at hardware stores and home centers) it has been made from all sorts of random wood waste, which is why it no longer has the wonderful scent that older people remember from decades ago. All forms are very toxic and best avoided. In old wood finishing recipes that call for it, mineral spirits (MS) can usually be substituted, but not always. For example Damar resin will not disolve in MS - there may be others. If the finish is just a mixture of turps and any kind of oil, most of the time MS can be subbed just fine (though less is used proportionally, as it is more thinning than turps).
An art supply company started producing many years ago a product they call 'Turpenoid', which is merely mineral spirits; nothing to do with turpentine at all, except that they intended it to be usd as a replacement for turps. Then they later came out with something called 'Turpenoid Natural', which has nothing to do with either turpentine OR mineral spirits, but is a mysterious, rather viscous solvent that seems to be some sort of mixture of orange oil and lord knows what else (great for cleaning dried paint out of brushes, though). Supposed to be non-toxic.
To confuse matters even further, some finishes call for
Venice Turpentine (which is from the larch tree), which really isn't a solvent, but an oleo resin. Much more common in oil painting mediums than wood finishes.
There are three basic forms of mineral spirits (sometimes called Stoddard solvent), which IS petrol-based (hydrocarbons): MIneral Spirits (MS), Odorless Mineral Spirits (OMS) and artist grade OMS, sold in art supply stores (I use Gamblin). OMS is more refined, has less smell (not really odorless), and evaporates more slowly so for a given length of time of exposure, less is inhaled. Artist grade (especially the Gamblin brand) is truly odorless and evaporates even more slowly so is the safest to use, as far as respiratory effects go.
I've always had the impression that White Spirits is mineral spirits, not alchohol.
Mineral oil and mineral spirits have nothing in common, except for being petroleum-based. Mineral oil is, well - oil; a lubricant.
Mineral spirits is a solvent that
dissolves oils.
For general wood finish, you should give this a try:
https://www.amazon.com/Wood-Welded-Emmets-Stuff-Finish/dp/B0000DD2S2It's an oil/urethane/wax blend, and very easy to apply - just rub it on and buff. Nice soft lustre.
Possibly the finest custom picture framer in the Western US, after many years of experimentation now uses this exclusively on his frames (mostly White Oak).
https://www.holtonframes.com/