So far as I know, the common usage is that a bucket or pail is a container for liquids (but may also be used for granular solids, like grain, etc.), without a lid, which has either a bail or handles on the rim to pick it up by. Also, a pail or bucket generally holds at least a gallon; five gallons more common.
A jug, pitcher or ewer is a container for liquids only and usually has a lip to aid in pouring. It may have a lid. In my understanding of the terms, the jug is the smallest, the ewer the largest (usually at least a quart and can be quite large).
However uncommon some of these terms may be, it gets even more outré when it comes to ecclesiastical usage. In Anglican churches, there is usually a good-sized (i.e., 1 to 2 gallons) brass ewer (that's the word used to refer to it) near the font which is filled with water. When a baptism takes place, the water is poured from the ewer into the font. The wine for communion is brought by the acolyte in one or more decanters (usually glass) to the deacon or priest, who then pours it into one or more flagons (yes, that's the word, otherwise archaic), which are small pitchers (usually silver) with hinged lids, holding maybe 2 cups. There is also a flagon of water. The deacon or priest pours wine from the flagon into a chalice, adds a small amount of water from the other flagon. On major feasts or other occasions when a large number of people (hundreds) are expected to communicate, there may be a silver ewer of wine instead of the decanter(s), holding a quart or more, from which the wine is poured into flagons. Interesting how various size containers are used and that archaic words are used for them.
