My nephew has lived in Oz for about 3 years now, and refers to cans of beer as "Tinnies" He has even started to use the the rising-inflection, which drives me MAD !
I don't think that the difference in terms is anything to do with the composition of the material used in the construction: most of have no idea anyway. I think the main factor is where you live. I've noticed that most people on this site use the term "tin", whereas in Canada and the US, the word "can" is used. But I imagine that there could be regional variations in UK usage. Also North Americanisms have a tendency to sneak over there.
'Can' is short for 'canister', which means a container. Cans were originally made of steel, with a coating of tin. Steel alone was no good for storing food, particularly acidic fruit juices, but a thin coating of tin prevented corrosion by the juices. So, cans became known as tins, because of the tin coating.
Beer and soft drink 'cans' are made of Aluminium. It is lighter than steel but more expensive. This is because the weight of it is important when people often buy packs of 12 or 24. 24 steel cans would be cheaper but too heavy to carry easily.
Tamborine both Aluminium and Tin have to be mined as do all other metals.
Steel is just Iron ( also mined) with some added Carbon.