"forgot your password?" .. why 'forgot"?

Hi,

Everyone knows how a typical logon procedure looks...
The user should enter their login and password, etc.
In a typical logon window we can often see a button called either "Forgot your password?" or "Forgotten your password?" , or "Forget your password?". (And "Forgot your password" is used far more often than the other two)

Now, to my question.

I understand that only "I forget" (= "I cannot remember") and
"I have forgotten" can refer to the present.
It seems to me that "I forgot" is very close to " I could not remember" and so cannot be used for "I have forgotten my password".

Please tell me where is the wrong link in my "train of thought" :-)

Thank you.

mus-te