Do people who claim that god speaks to them suffering delusions or are just close to god?

There's a line, but: Gnenerally, the answer is delusional. People can feel very close to their god, and each one can define what that is for them. This closeness certainly involves their communicating with god. However, when that communications translates into actually hearing statements or commands that they feel are real (like the kid that killed john lennon), then it is delusional, it is part of a psychosis.

Beautiful mind: Watch the movie beautiful mind - actions speak louder if that person can engage well in day to day activity and understand consequences of behavior then does not matter if they converse with god. The only thing that separates sanity from insanity is understanding consequence. I say this before handing out pink slip. If one consent to being observed might avoid a pink slip.

It depends: Discerning such things requires openness and empathy. When saying that god speaks to them, many mean through inner urging or inspiration, rather than an actual "voice" experienced externally. When there's an external voice commanding dangerous or harmful actions towards self or others -- it's more likely delusional. Another marker is if it's very different from the person's usual culture.

Depends. : If you require evidence for your beliefs then. You would consider them delusional. That's what the evidence suggests. But if you are willing to believe anything without proof ( faith) then you can believe anything you want. ... including that they are really close to God