As I understand it (and I'm sure others will correct me)a Gael is a person who speaks a language from the goidelic sub-branch of the Celtic languages i.e. Manx, Irish Gaelic and Scots Gaelic.

A Celt I believe speaks a language from the brythonic sub-branch of the Celtic languages i.e. Welsh, Breton and Cornish.

The goidelic sub-branch is the older version of the language, a form also known as q-Celtic on account that (to take Irish as an example) cúig, five and cuathir, four begin with a hard "c" sound as compared to the younger p-Celtic languages (i.e. brythonic languages) where (to take Welsh as an example) pump, five and pedwar, four begin with a "p" sound. This q/p distinction is one of the distinctive features of the differences between the two sub-branches.

I should imagine that the terms Gael or Celt may still be applied to those who do not speak the Celtic languages as long as they live in areas where such languages are widespread, or feel that they have more affinity with their Celtic brethren, as opposed to their English or French speaking neighbours. However, this is only my opinion!