Are pegacorns and alicorns the same thing?

[knuckles 150]

i think alicorn is a term for pegacorn in the mlp universe

[Everleaf 541]

Well I would like to see this looked into within the show to give a good example (even if so pegacorns are not canon) as this would be quite interesting... though writing may not be the easiest by this... well this is why headcanons are around I suppose...