UI Terminology: Logon vs Login [closed]

Since you're looking for correctness,

login, logout, logon, and logoff are all nouns:

"Please enter your login credentials."
"I see three logons but only two logoffs from this user."

The corresponding verbs are each two words:

"Please log in to see your reputation."
"You must log off and talk to a human."

Update: according to dictionary.com, the various definitions of login are all nouns and involve gaining access to a computer or computer service. Interestingly, logon redirects to login as an exact equivalent. Have the definitions evolved?

Voice of democracy: term / number of google results:

login    2,020,000,000
sign in    430,000,000
logon       27,700,000
log on      18,200,000

logout      83,500,000
log out     34,500,000
sign out    19,400,000
log off      5,350,000

Logon is used for a hardware system that starts up when used, like a computer.

Login is used for a software system where I have to enter my username and password.

Signin is used for identification, either physical such as a photo ID, or digital such as OpenID. What differs here from login is that in the case of an ID, I can use the same ID to access multiple sites, buildings, etc.

Edit 1: I should've added a disclaimer that I have no sources and make no guarantee that these are the official usage of the words. The definitions I'm offering about are based on my personal understanding of the usage, and are purely opinion.

with spaces:
http://google.com/trends/explore?q="log in","log on","sign in","sign on"
winner: "sign in"

no spaces:
http://google.com/trends/explore?q=login,logon,signin,signon
winner: login

spaces vs no spaces:
http://google.com/trends/explore?q="sign in",login
winner: login

with spaces:
http://google.com/trends/explore?q="log out","log off","sign out","sign off"
winner: "log off"

no spaces:
http://google.com/trends/explore?q=logout,logoff,signout,signoff
winner: logout

spaces vs no spaces:
http://google.com/trends?q="log off",logout
winner: logout

My preferences (less popular, but many cool websites are using this convention):

[Sign In] [Join]

Welcome, UserName! [Sign Out]

I wouldn't use any of the following: Log On, Logon, Log In, Log Out

Another option is (which is by the way more popular):

[Login] [Register]

Welcome, UserName! [Logout]

Google Stats (hits):

[Sign In], [Sign Out] -> 1 210 000 000 + 300 700 000 = 1 510 700 000
[Login], [Logout]     -> 1 940 000 000 + 88 200 000  = 2 028 200 000
[Log In], [Log Out]   -> 873 000 000   + 83 800 000  =   956 800 000

[Sign Up] for registration link is also a good option but it does't look good near [Sign In], you should use it wether with [Login] or seporatly.

[Sign In] [Join] on a page looks more user-friendly (less official) for me than [Login] [Register]