"Spelling checker" or "spell checker"?

I've always thought a spelling checker is a tool that checks spelling. I know a growing number of people say spell checker, but I've always considered that slang. Recently I did a search for the term and saw that many professionally-edited outlets use the shorter version. Has the shorter term become acceptable in formal writing?

Does it generalize to the verb form as well?

1. I need to spell check my document.
2. I need to check the spelling in my document.

Spellcheck and spellchecker are both in Oxford Living Dictionaries, on line.

I've usually seen it used in combination form: spellchecker. The verb is spellcheck and it conjugates the same way check does. It's also used as spell checker, and I guess you can take your pick.