What are the differences between third-party base maintenance, line maintenance and component maintainance?
Base maintenance: The maintenance work is done in a hangar, with special tools and equipment. Third-party just means that someone else than the operator of the aircraft is running the shop.

Line maintenance: The work is done on the flight line, basically on the apron out in the open.

Component maintenance: The work is done on some component that had been removed from the aircraft before. Typically, this item had been swapped against a good one in line maintenance and is now looked at in detail in a specialist shop. Items like this are called LRU (line-replaceable unit). Components could also be as large as a whole engine which needs to be serviced in a special shop and is removed during base maintenance.