What made Parliament able to raise money in a way the King couldn’t? Did the King simply need their approval to raise taxes or was it more complex?
I can answer this from a more Late Medieval and Early Modern view, and your example is in the end Medieval transition.
The important thing to understand is the king was originally sort of a Big Lord, rather than a clearly different thing. They were often held to the same or similar expectations. And their role became more differentiated as they changed and expanded over time. The English crown personally held the Duchy of Lancaster, and other feudal dues and rights. They were expected to be somewhat self-sustaining, without drawing on tax money much for personal needs. Taxes were conceived as primarily for war and other emergencies, so it was necessary to call parliament for them (partially because of baronial resistance in Plataganet history that often utilised parliament).
This particular situation is why parliament did not sit every year or for the exact same time each parliament. It was called fairly regularly whenever taxation was needed but also not expected to be called too often. Parliament, while it gained increasing ability to make significant laws, was not considered part of the regular governence of the country. When it was called, it was usually specifically for the purposes of raising taxes, during the Tudor times mainly through what was called the subsidy, which was a graduated income-based tax that unfortunately became less accurate over time, as well as the older fifteenths and tenths, and it would be dissolved when it was no longer needed.
So the ability to pass laws in parliaments was somewhat opportunistic. In some ways parliament benefited from generally agreeing to raise what the crown requested, because it made the monarchs more willing to call parliaments and give them the opportunity to use those other powers. When parliaments were particularly uncooperative with funding, they tended not to summon one again for a while.