Look at the leaves. birch leaves and cherry leaves are very different.

The bark is usually very different also, except that both can be shiny and smooth.

Not wanting to put words in your mouth, maeve, but birds love cherries of any kind and cherry sprouts from bird poop are common. When trees are cut down without the stump being removed, they often coppice, which means sprouts grow up from the trunk or immediately adjacent roots. Where there are trees, there are usually birds that perch and poop. Many bird species eat (in the southeast both choke and black cherry are native and common) cherry and cedar fruits. It is not rare at all for assorted cherries or eastern red (I don't know about eastern white) cedars to grow snug up against the base of another species. If the other species is cut down, the bird-sown other species can be even more opportunistic.