Firkin is the word for today, and sometimes you will hear the term "sugar firkin" used as well. A firkin is a bucket used to store sugar, and it was made of wood, typically with a swing handle and a unattached lid. The most desirable firkins have original paint and are coveted by early American primitive collectors. My examples are either unpainted or have been stripped of their paint which decreases their value:
Most firkins you will find have similarities, such as the "finger bands" that wrap around the staves, the staples that hold the finger bands, and pegs that hold the swinging handle.
A sugar firkin like the examples in this post with a lid would sell for about $125 on up here in Michigan. With the original milk paint it would be much more valuable.