These are related to MROs(Maintenance, repair and operations) activities ?
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.
These are indeed related to MRO activities.
Line maintenance generally refers to minor, unscheduled or scheduled maintenance carried out on aircraft that occurs at or near the gate or terminal (Tarmac), launch area, ready area, hardstand or alert area. This is usually carried out by the operator. This is the basic level of maintenance and is limited by the ground support equipment available.
Third Party Base Maintenance refers to the base maintenance (i.e. maintenance done in aircraft hangar with special tools) carried out by a third party- other than the manufacturer and the operator. This is usually the next level of maintenance.
Component maintenance refers to the maintenance carried out on some component removed from the aircraft (for e.g. rotable or LRU) due to fault or completion of specified service time in a dedicated shop or lab. These are usually done for avionics units, engines, transmission items etc. This is usually done by the OEM or their authorized agent.