They overlap almost completely — both mean "in any case" or "regardless". Anyway is far commoner and works in every context; anyhow sounds more informal and slightly regional, and has a second sense of "in a careless manner" that anyway lacks. The one thing to avoid is "anyways", which is non-standard.
The core difference
As discourse markers they are interchangeable: Anyway, we should go and Anyhow, we should go say the same thing. Anyway is the default; anyhow reads as more casual and is commoner in some regional varieties.
The sense anyhow has to itself
Anyhow can mean carelessly or in a disorderly way — "the books were piled anyhow". That use is chiefly British and somewhat dated, but anyway cannot substitute for it.
What both do in conversation
Their main job is managing a conversation rather than adding meaning:
- Returning to the point after a digression: Anyway, as I was saying…
- Dismissing what came before: It was expensive. We bought it anyway.
- Closing a conversation: Anyway, I should let you go.
Anyways
Standard English has no anyways. It is common in speech in parts of North America and appears in informal writing, but it will be marked as an error in edited prose. The same applies to anywheres and somewheres.
Any way, two words
Spaced, any way means by any method: "Is there any way to fix it?" Test by inserting a word — "any possible way" — which works for the two-word form and breaks the one-word one.
Frequently asked questions
Is "anyways" a word?
Not in standard English. It is common in informal North American speech but is marked as an error in edited writing. Use anyway.
Is there any difference between anyhow and anyway?
As discourse markers, no. Anyway is far commoner; anyhow is more casual and also has a sense of "carelessly" that anyway lacks.
When is "any way" two words?
When it means by any method: "Is there any way to fix it?" Test by inserting a word — "any possible way" — which only works for the spaced form.