We understand, but as far as I know <em>never</em> say "a tin." It is always "a can." However...

1) It is becoming rarer, but we <em>do</em> use the collocation <em>tin can.</em> I think <em>can </em>shortened form of <em>tin can. </em>I wonder if this is a case where US speakers dropped one word and British speakers dropped the other. Here are some examples in which "tin can" is the only natural thing to say.

a) It is a myth that goats eat tin cans.

b) McGyver improvised a working cyclotron out of chewing gum, flashlight batteries, and old tin cans.

2) For some reason, aluminum foil is very commonly referred to as "tinfoil."

3) I agree with others that I've heard the phrase "baking tin."

Sheets of tin are easily shaped, so we do have a variety of expressions in which "tin" is used to suggest something cheap and shoddy.

I can’t think of a single use of “tin” or “a tin...” that way. I recognize it as a British use for things like tinned meat, etc but we don’t say that. The closest I can think of right now is “tin can” and “tin foil” for a can of food and aluminum (aluminium) foil. But both are archaic now and falling out of use. They’ve been made out of steel and aluminum for long enough apparently.

The historic origins of the use of the word tin that way coming from kitchenware and many household goods being hand made out of tin is interesting though.

I hadn't thought much about 'tin' or 'can' before reading this discussion.

I suppose the well-known slogan from a UK television commercial by a manufacturer of [cans of] surface coatings, etc for household and hobby use would not be understood in the US :

"It does exactly what it says on the tin".

Tangentially... but I love this passage. This is from <em>The Virginian,</em> a novel by Owen Wister that set the pattern for the "Western" as we know it. It was published in 1902, but set in 1880s Wyoming. The narrator arrives by train in Medicine Bow (and finds that his luggage has been lost).

<em>Morning had been for some while astir in Medicine Bow before I left my quilts. The new day and its doings began around me in the store, chiefly at the grocery counter. Dry-goods were not in great request. The early rising cow-boys were off again to their work; and those to whom their night's holiday had left any dollars were spending these for tobacco, or cartridges, or canned provisions for the journey to their distant camps. Sardines were called for, and potted chicken, and devilled ham: a sophisticated nourishment, at first sight, for these sons of the sage-brush. But portable ready-made food plays of necessity a great part in the opening of a new country. These picnic pots and cans were the first of her trophies that Civilization dropped upon Wyoming's virgin soil. The cow-boy is now gone to worlds invisible; the wind has blown away the white ashes of his camp-fires; but the empty sardine box lies rusting over the face of the Western earth.</em>

So littering was common then. Imagine movie cowboys riding along littered trails! Anyway, my point is that foods were "canned," but the rusty sardine container was "a box," not "a can." Today we would always call it "a can of sardines."

I can't think of a modern American use of the word "tin." I do remember "tin can" (for a steel can of soup) and "tin of tea" being used by my grandmother in the 1960s.

Of course, there are 300 million English speakers in the U.S. and Canada. I can't speak for everyone.