The 2nd one is "default"? In the U. S., I don't I've ever seen a peeler that wasn't like your first link. That, or I just never recognized the second link as a peeler. Looks kind of like a cheese slicer to me. :-)
In my experience the straight style is more ergonomic for carrots and parsnips whereas the Y-peeler works better for potatoes, citrus, and other roughly spheroidal foods.
(I also use my [very sharp] Y-peeler for shaving hard cheeses into flakes so sure, I guess it is a cheese slicer too :) )
I like to cook with my child, they were able to peel carrots at age three using one, albeit with me holding the carrot!