1.  Recall:  The vehicle is recalled to repair what has been determined, (usually by the federal government) to be a safety hazard or something causing emissions standards to be violated.  The manufacturer is obligated to pay 100% of the cost, but watch out for a dealer that uses the recall as an opportunity to recommend a huge list of services that will add up to considerable expense and all too often serve no purpose.  There is no time or mileage limitation on a safety recall.  “Salvage title” vehicles that should have gone to the scrapyard may not be covered.
2. Technical Service Bulletin:  This is information published by the vehicle manufacturer as to what is a likely cause of a vehicle malfunction with recommendations on the course of repair.  The fact that a problem is described in a technical service bulletin does not obligate the vehicle manufacturer to cover the expense of the repair, although the manufacturer might volunteer to do so.  See below.
3. Warranty Extension:  While this may have been negotiated as part of a recall — see #1 — it is typically an offer by the vehicle manufacturer to appease the public when there have been egregious failures in some part of the vehicle.  This could be something like covering the cost of an extremely expensive digital display screen for  a much longer period than it would be covered by the basic vehicle warranty.

When researching a vehicle problem on the internet, it frequently seems like “They all do that!” But the percentages are not what they seem.  Typically for everybody who posts a particular problem there are hundreds or thousands of owners of the same make and model who have not experienced the issue with their vehicle.