The Base Check (OPC/PPC) is a look at your ability to carry out emergency manoeuvres at your normal flight station, plus your flying technique and IFR procedures. It's valid for 6 months, plus the remainder of the month of issue (actually, that's not strictly true for UK - you need two every year, at least four months apart). It's needed for each aircraft and, although the statutory requirement is to assure your continued competence, it's also used for training, as it's a good time for practising drills and procedures that rarely arise in normal operations. It also includes an element of CRM, as do many others.
The line check This is valid for 12 months plus the remainder of the month of issue, but if you take it in the final three months, you can extend to 12 months from the previous expiry date. It's a test of your performance of normal duties at your crew station, so will be done on a standard commercial flight, or at least the final line check will (initial ones only give you the status of 1st pilot under supervision). It covers an entire line operation from pre-flight preparations to completion of post flight duties and normally must be carried out on each type of aircraft flown, although it may be done alternately where types are similar. It's not supposed to represent a particular route, but must be an adequate representation of the Company's work. Line Checks may be carried out by fully qualified Line Captains.
Line training, leading up to the check, is supposed to familiarise you with the routes over which you will operate, for which you will be supervised by experienced training staff. Before you can do this with passengers, you must have passed an initial line check, followed by some supervised flights, then a final line check before they let you loose on the unsuspecting public.
Supervised flights will have passengers on, so you will now become aware of commercial pressures, and are as much a hurdle to some pilots as other training is, because you will probably also have Flight Director systems to use - you normally don't get to use them in training.
Phil