While all thrum caps are fuzzy, but not all fuzzy hats are necessarily thrum caps. There were many kinds of hats with fuzz, pile, or loops during the 15th and 16th centuries.

The Bristowe hat in the Royal Ceremonial Dress Collection is attributed to Henry VIII, and consists of a wool base covered with individually tied silk thrums. Tying off the the thrums is necessary for silk because silk is slippery, while the microscopic “scales” on wool thrums lock them in place when the hat is fulled.

Silk-thrummed garments were apparently an ongoing thing in Henry VIII’s attire, since there are descriptions of him wearing wearing silk-thrummed hose as well.
“The king being in his dublet and hosen, all of sheepe’s colour cloth, his hosen, from the knee upward, were thrummed very thicke with silke of the same colour.”
– The Life and Death of Cardinal Wolsey, George Cavendish, 1558
Some Mamelukes wore tall, shaggy hats of red wool called “Zamt”, starting in the early 15th century. These look intriguingly similar to the earliest depictions of thrum caps in Europe, which are found in Italian art and show tall red shaggy hats on figures meant to seem exotic.
“… and wears on his head a high red hat, without a brim, about three spans high, with long wool hanging from it about a span long.”
– Arnold von Harff, prior to 1505

There are also several wool felt hats in Irish museums that were found preserved in peat bogs, generally attributed to the late medieval period. These don’t appear to be knitted, and seem to be a very different
We also have several “imitation fur” hats found in high status graves from the Bronze age, constructed of individually tied threads.
