prepositions - 'On the computer' vs 'At the computer'

Are they all grammatically correct and do they all have the same meaning ?

1. 
   

   She was on the computer writing an email a minute or two ago.

   
   


2. 
   

   She was at the computer writing an email a minute or two ago.

   
   



3. 
   

   She was writing an email on the computer a minute or two ago.

   
   


4. 
   

   She was writing an email at the computer a minute or two ago.

   
   

Answer

Literally speaking:

Cat on the computer:

Cat at the computer:

However, someone might be said to be "at the computer" just meaning that they are physically at the computer station without necessarily using it:

And they might be said to be "on the computer" meaning that their attention/activity is on using the computer: