In simple words, When someone sends you an SMS, that means he/she pushing SMS to your phone. When you are requesting for some SMS from sender and you received the same, then you are pulling SMS from the sender to your phone.
Any message origination from the server without a request from the receiver mobile is PUSH SMS. Eg: You get SMS alert about offers, announcement from bank, balance info when you withdraw money from bank, etc.
Any message originated from a mobile device and received at server end and server responds with the available information, then it is PULL SMS. For eg: You checking score by sending a request to 56677, You checking balance of your bank account by sending your account number to 51234, etc.,