From what I've encountered in spoken and written German so far, I can see two cases:
- Literal meaning: "auf jeden Fall" can mean literally "in any case" or "always".
Auf jeden Fall musst du nach links und rechts schauen, bevor du über die Straße gehst.
meaning
In any case you have to look left and right before crossing the street.
- Filler word: "auf jeden Fall" and "jedenfalls" are sometimes used to start a sentence as a filling word. This is mostly used in spoken, but not in written language:
Jedenfalls bin ich dann früher nach Hause.
Auf jeden Fall bin ich dann früher nach Hause.
meaning
Anyhow, I went home early.
"Auf jeden Fall" can be used literally and as filling word, "jedenfalls" only as latter.