I think we use bar & measure interchangeably in the the US. "Bar" and "bar line" are also synonyms.

Brits call the written out music 'dots.' I don't think we have an equivalent, sheet music, maybe. I think dots is really useful.

US & UK use movable do & name the notes A to G. French & maybe others use fixed DO. C=DO, D=RE, etc.

16th & 32nd notes are much easier to understand than the British equivalent. I've seen the UK terminology in some 19th century books. I wonder if our US practice is a translation of German terms. I know German musicians had a huge influence in the early 19th century.