Yes. I've never heard a counselor suggest that a man keep a diary, however, the suggestion of a journal is common. Women and girls have "journaled" their lives for generations in what is called a diary. I never have known a boy to do so but that doesn't mean they don't/haven't. But men do keep journals and history has given us some good examples of that.
I'd say no... they are fairly similar things and many people would use then interchangeably... It's true that *some* counsellors etc *may* differentiate if they feel that *some* of their clients have a particular over-sensitivity towards certain expressions, i.e. an insecurity about their masculinity. I keep a *journal* or am supposed to. I see maybe a slight difference in that a diary is perhaps more personal, and a journal perhaps more specific; recording triggers etc...
By way of evidence I offer Samuel Pepys diary, note diary.
There may be a slight preference re language, I definitely DO think of the word Journal as being more an *American* word. Wall Street Journal, and stuff... It has a kind of alien ring to it to me...but is a word that has crept in over here in recent years.