It is the same verb:
Vult is 3rd person singular indicative
Velit is 3rd person singular subjunctive
So, vult= he/she/it wishes/wants and velit= he/she/it would wish/want, that sounds more natural as "would like"
A literal translation is rarely good, and a good translation is rarely literal
Here is the indicitive present conjugations of Nolo, Nelle- to be unwilling/to wish not to
Nolo / nolumus/ Non vis / non vultis/ Non vult / nolunt