How can I tell between an apple and crab apple tree?

A 'crab' apple is simply a wild apple tree, although there are specific varieties like John Downie, Golden Hornet etc. Lots of named varieties of apple started from pips, and are known as 'Seedlings' as in Bramley's seedling.
So there really isn't any difference except that generally 'crabs' have smaller fruit which are acid or not very sweet.
If the fruit on this little tree is edible it may be just a chance seedling which has luckily come close to its parent.
If not, like most 'proper' apple trees it will have been grafted. Look low down on the stem to see if you can see if it has been grafted by the bulge where the root stock and the grafted wood have united.
Sorry for such a wordy reply. I always did suffer from verbal diahorrea!

Bertiefox: We ask questions because we want a reply. In this case, the more information the better. Never stop with the wordy replies! They are certainly apreciated from me.