To start with, arms were a free-for-all. Eventually the Earl Marshal was put in charge of regulating heraldry in England (Scotland has its own arrangements). The title of Earl Marshal became a hereditary possession of the Dukes of Norfolk (still is). The Earl's courts would hear complaints.
Later (around 1490), the College of Arms was set up with the Earl Marshal in charge. It was established that only a gentleman could bear arms, and the heralds at the College had power and discretion to decide who was a gentleman.
It was laid down that usage was sufficient evidence of entitlement - you could show your right to a coat by showing that your ancestors had used it. Most people had nothing else then.
But it was never clearly stated that this was only intended to apply to ancient arms from the pre-College era, before official records were kept. As a result, 19th-century armchair lawyers would claim "usage" for the arms unofficially adopted by their 18th-century ancestors.
William III had found a technical way to suspend the Earl Marshal's courts, so although the College retained its authority on paper, it became a toothless bulldog. It's now been sold off to private enterprise and is just a commercial operation giving the customers what they want.
Nor was it ever explicitly stated that the heralds could grant new arms to upwardly-mobile nouveau-riche plebs. They often did, but they liked to cover their tracks with some sort of fig-leaf. So it was never officially admitted that gentry didn't need blood, money would do the trick.
Early Visitation pedigrees often start with "a second brother out of the house of" or just "came out of Yorkshire". This basically means "no idea where this lot sprung from, but the dinner and the wine were up to scratch, so they're in".
So arms were always hereditary, but only to descendants of the original holder, not collaterals. In the case of the nouveau-riche, the grantee was often just one member of a sprawling clan.
And descendants who descended into the ranks of yeomen and below were expected to drop the pretension of gentility when they didn't have the money to support it.