Questions regarding the Falcon launch vehicle developed by SpaceX for medium payloads (15,000 lbs) to LEO and GEO (via GTO, second stage cannot inject into GEO direct)
Developed by SpaceX, the initial Falcon 9 version used 9 Merlin-1C engines in a tic-tac-toe layout on the first stage and a Merlin 1C with a vacuum nozzle for the second stage.
After the first five launches it was replaced with the Falcon 9 V1.1 or F-9R (R for reusable). The engine was upgraded to the Merlin-1D which due to higher thrust consumes more fuel and oxidizer, so the first stage tanks were stretched to provide more consumables. The engine layout was changed to a circle of eight engines, with the ninth in the center, known as the Octaweb layout.
A further improvement informally known as the V1.2 configuration, but officially as the Falcon 9 Full Thrust increased the thrust of the Merlin-1D engines again, using subcooled fuel (RP-1) and oxidizer (LOX). This extra performance allows for recovery of the first stage on most missions.
The first stage got landing legs, which are used to recover the first stage on land with propulsive landing. Three engines fire before reentry to the atmosphere to slow the booster stage and a single (center) engine is used for actual landing.
For missions with spare performance, the stage can boost back to the launch site and land on land. For those without sufficient performance left after the mission is launched (most GTO missions) the stage can land on the ASDS Barge (Autonomous Spaceport Drone Ship). SpaceX has one deployed in the Atlantic Ocean (Marmac 303 — "Of Course I Still Love You" or OCISLY) and one in the Pacific Ocean (Marmac 304 — "Just Read The Instructions" or JRTI).