Glycerine is identical no matter where it came from--animal, vegetable, or mineral. Glycerol is just another name for it.
Whether I produce glycerine when soapmaking using coconut oil, palm oil, or rendered pig fat doesn't make any difference to the molecule (it does to the amounts of lye used to break the triglyceride into glycerine and soap, however, as the saponification index differs for each fat used). A chemist can't determine the difference between them (there is no difference) given only a sample of the resulting glycerine. One could, of course, if given the entire soap.
However, to call it vegetable glycerine it has to have a 100% vegetable oil used in production.
Fun fact: The story about glycerine crystallation that floats around (just cool to 17 C!) isn't true. The uncrystallized glycerine in my fridge, at 1 C, puts the lie to that one!