No it's not the same.
A limey is a good hearted nod to a naval tradition.
A yank is a good hearted nod to a book.
A pom is allegedly a contraction of pomegranate - pronounced to rhyme with immigrant ( I guess your accent has to be right for this)
It's a slur applied to all brown people, regardless of heritage, a way of othering and dehumanising people.
In short, it's racist, don't do it, don't make excuses for it.