There are 2 types of tickets you can buy to visit the Eiffel Tower:
Eiffel Tower stairs ticket that you can purchase either online or on the spot. The Eiffel Tower stairs ticket composes 2 different tickets:
2nd floor stairs ticket which includes going up to the first and 2nd floor Eiffel Tower by stairs. It is excluded the summit/top floor entrance ticket
Summit/Top floor Eiffel Tower ticket by stairs: It incluedes all the way up. So you will visit the 3 platforms of the Eiffel Tower. Once you hold the entrance ticket, you have to climb to first floor and then to the second floor of the Eiffel Tower. There is no way to go up to the third floor/summit/top by stairs. Therefore you have to take the elevator from the 2nd floor to summit to go and down. After you finished visiting the Eiffel Tower, you can either take the stairs to leave the Eiffel Tower or the lift.