In case you're wondering how I can be so confident that it is only the battery; the car's electrical system cannot tell the difference between when the battery supplies starting power, or when it comes from a jump start. If a jump start will start the motor every time; a good battery will also.
However, there is one condition where this does not hold true. And that is when the battery cable clamps are either not tightened, or are corroded on the inside surface. This corrosion is often not visible to the eye; but it will effectively insulate the cable clamps from the battery posts. When that happens, the battery is blocked from sending enough power through the cable clamps to run the starter; although it often will be able to supply smaller amounts of power, such as are needed to run lights. In a situation like that; connecting jumper cables to the battery bypasses the blockage from the corrosion, because the jumper cables connect directly to the battery cable clamps. So a jump start will supply enough power to run the starter, when the battery is either weak, or a good battery has bad cable connections.
One of my friends has a car that becomes unable to start every few months. And I have shown him that all it takes to make the car start reliably at those times is to remove and thoroughly clean the cable clamps and battery posts with a battery cable service tool. So now his car no longer leaves him stranded when that happens.