I don't know all the American/British clothing equivalences, but here
are a few:

American British
vest waistcoat
undershirt vest
underpants pants
pants trousers
running shoes trainers

I've not been following the camisole, tanktop, sport bra, training bra,
.... discussion very closely (not likely to be very relevant to my son,
even though we do live in California).

There are some equivalence lists on web---for example,

http://www.free-esl.com/gg/englishes/ambrvoc.htm
(has some errors, like about what "shorts" means in
American English)
http://www.geocities.com/Athens/Atlantis/2284/
http://www.centripedus.com/amlish.html
http://vocabulary.englishclub.com/voc-ukus.htm
(has several errors in usage)

--
Kevin Karplus http://www.soe.ucsc.edu/~karplus
life member (LAB, Adventure Cycling, American Youth Hostels)
Effective Cycling Instructor #218-ck (lapsed)
Professor of Biomolecular Engineering, University of California, Santa Cruz
Undergraduate and Graduate Director, Bioinformatics
Affiliations for identification only.