"See you later"...which one is which?

[valhalla]

I was checking that what I had for "See you later" was correct and I found many different people and sites saying conflicting things. There is a Youtube video at https://www.youtube.com/watch?v=bHctS8erhx4 where the girl is telling us that "See you later" is De veo despues and she even has it written on the screen along with the pronunciation...[day-Vay-o Des-pwace] But when I Google De veo despues it does not find anything and in fact it corrects it with Te veo despues. I cannot find De veo despues anywhere. In the comments of the Youtube video people are correcting her saying it is Te veo despues. Then I'm finding the following also for "See you later" : Hasta luego, Te veo luego, Nos vemos and who knows how many others. I realize you cannot necessarily do a direct translation but this phrase is all over the place. I would like to know what people in Spain say that is the equivalent to "See you later" which to me is a casual way of departing like with a friend that you probably will see sometime relatively soon, kind of like "Take it easy", which has a similar "flavor" or effect but really means something different.

Can someone please clear this all up for me with details of literal meanings and what thought is being expressed by each etc.?

Gracias!

Valhalla