Turps usually means 'turpentine substitute' which is just another name for white spirit. Turpentine is the lovely smelly stuff used with artists oils and is waaaay too expensive to use for routine thinning of varnishes and stains ( which is what the AP dip is). White spirit should work just fine, and the cheap variety from B&Q or wherever should be just as good as any other.
More or less right, turpentine is a product derived from some type of conifer resin, which is why it has that strong smell. White spirit is a petroleum fraction close to paraffin or lamp oil. So Wikipedia gets it right for once Both are technically 'organic' though in the chemical sense of the word, as opposed to the sandal wearing, bunny loving one.
The thing with turpentine though is that it is an unholy mixture of all sorts of stuff so the chance of an adverse reaction with the dip is much higher. White spirit, while still a mixture of chemicals, is all pure hydrocarbons, and is what is used to manufacture the dips in the first place.
Well I personally will keep using my artist grade white spirit as it is purer and the spermarket stuff. After all there must be a reason why artists prefer this stuff over the cheap stuff otherwise they wouldn't bother to make it
I have used AP dip on 15mm figures slight from the can, works just fine. Do NOT dip though, instead use a brush to paint the dip on. After 5 or 6 figures go back to the first and use 'empty" brush to take off any pools or blobs, repeat after every new figure until whole unit done. Great for horses at this scale as well....