The difference is that Veblen goods are luxury goods whereas Giffen goods are inferior goods (https://en.wikipedia.org/wiki/Inferior_good).

Well, the mechanisms are generally different too. Giffen goods can exist even for simple models with homoeconomicus. Veblen good generally involve a signaling/status story.

Both have a behaviour resulting from the purchaser's cost constraints.

One important difference is that Giffen goods probably don't actually exist in the wild given that they depend on a somewhat contrived substitution effect.

Similar in that supply-demand behaviours are pardoxical, though for different reason, at least topically.

Considered as an informastion and signalling good, Veblen goods start more closely resemblin Giffen.