The size indicated typically refers to the threaded pipe size, but in
the cases of hoses it refers to the hose's inside diameter. Most typical
3/8" hose assemblies (from HD, Lowes, etc) will come standard with 1/4"
pipe threads, specialty hose assemblies from major air tools suppliers
and maybe the HD, Lowes will offer a 3/8" hose with 3/8" pipe threads.
And in special case you can fine a 1/4" hose assy w/ 3/8" pipe threads.
The best way to go now days with the high flow rates of air
grinders,sanders is to go with the high flow couplers and 3/8" hose with
high flow 1/4" ends. What I have done is buy standard 3/8" hose w/ 1/4"
ends and drill out the 1/4' fitting to 5/16" or there abouts, . Harbor
Freight is an excellent place for high flow air fittings. I believe HD,
Lowes have a limited selection too.