How does a bottle differ from a jar?
English is unusually, perhaps uniquely, rich in its selection of
words for similar things. But I find that my own sense of the meaning
of a word is often narrower than its full formal meaning.
For example, a bottle in my idiolect has a screw top which is much
narrower than the body of the vessel; it's significantly taller than
it is wide; it's probably made of glass (though as I look around most
of the bottles I see are plastic). A jar is a bit shorter, and has an
opening that takes up most of the width; and a tub is wider than it is
tall, and may not have a lid at all. All of these things are basically
cylindrical (pace Jack Daniels).
Meanwhile among the cuboids, a box has a lid that's probably intrinsic
(or at least it used to have one); a crate might well have a separate
lid, but probably doesn't; a basket is unlikely to be wickerwork but
at least has pierced sides. If it goes into or is arranged into
shelves and gets pulled out for use or has an open front, but isn't a
permanent installation like a drawer, it's a bin.
And then there are the large lidded plastic storage boxes which aren't
unambiguously described by any single word. Storage boxes, storage
bins, the tubs in the garage.
(And a "tin" is usually the small cylindrical food container, now
usually with a ring-pull top; but a box of chocolates or biscuits, or
the container in which the tea is kept, can also be "a tin",)
What I am unlikely to do is reach for the generic term "container".
Meanwhile my wife refers to anything smaller than a skip or a shipping
container (which is what she thinks of first when "container" is
said) as a "dubby", which her father brought back from military
service in India; it's probably from "dubber/dabbah" (southern Hindi
from Persian), a container (traditionally of buffalo hide) in which
ghee or oil can be transported. Wiktionary suggests that this meaning
descends ultimately from Arabic دُبَّاء (dubbāʔ, “bottle gourd”).