I have successfully received my ship and I can see it in my hangar, but I can't find it in-game or I have a completely different ship in the game?

Star Citizen is still in the alpha phase and many ships have not been released into the game yet. So if the ship that you’ve purchased is not flight ready (released in the PU), you will receive a “loaner ship” that you can use until your ship becomes available. Please find a list describing what loaner ship you will receive here.