What's your feeling about those two?
There is no difference in meaning between the two. "Hit the enter key" sounds a bit more formal, while "hit enter" sound more colloquial. In a spec, I would expect "hit the enter key," but in the end, I dont think there is much between the two.
I'd say "Press the enter key", since saying "hit" will get a certain type of user needing to replace their keyboards fairly frequently.
I don't see a difference between the two, but depending on the context would choose which to use. If you're writing documentation or directions telling somebody what to do. I think I would choose a more written out version. Or like Paul suggested, "press the enter key" might be more appropriate.
To a non-technical user, "hit enter" is meaningless. You might as well say "slap leave" or "punch ascend" for all the good it will do them.
Also note that the Enter key is typically the one on the numeric keypad, while the one on the alphabetic section is Return - although that is not always the case (especially on laptops which do not have dedicated numeric keypads). If you tel the user to use Enter, make sure that pressing Numeric-keypad Enter actually works!
If you expect less technical users to use your program, a variation on "Press the Enter or Return key to continue" might be a more user friendly wording.
But if you know your audience is tecchy, then "hit enter" is perfectly adequate.
Microsoft Manual of Style Third Edition shows the example "Type your password, and then press Enter." No "key" at the end, and they put key names in bold. (p.254)
Sun's Read Me First! style guide says the same (p.60-61) but they don't put Enter in bold.
IBM's 2009 style guide has the same convention as Sun. (p.154)
Apple's 2008 style guide uses "Enter key". (p.66)