tl;dr: "cream," means heavy cream or half-and-half.
For context, I live in the US.
If you visit my house and ask for cream in your coffee, I will give you heavy cream. I suppose it is possible to find light cream in the US but this is so exceedingly rare in a normal supermarket that we'd normally say it doesn't exist.
Half-and-half (approximately 1:1 cream and milk) is very common and it used in many restaurants to replace cream. It is common largely because it gives much the same feeling in one's coffee as cream but is significantly better on the health. If I had this, I would give it to you and consider it equivalent to cream.
If I didn't have cream but I had milk, I would tell you that. Most likely, I would offer by milkfat percentage I have available: whole, 2%, 1% or skim.
If I didn't have milk, I would tell you what else I have that may substitute. Lactose-free milk is increasingly common and even more so non-cow milks such as almond, oat, coconut, etc. (Soy milk, on the other hand, has nearly disappeared from American supermarkets due to an irrational fear of soy products.)
I would not offer you creamer, mostly because I drink my own coffee black and I don't ordinarily have fresh creamer on hand. Much of the creamer available in this country is sweetened and artificially flavored, French vanilla and hazelnut being very common. I have met social groups where putting this sort of creamer in your coffee is de rigueur but I cannot recall anyone who has ever called this, "cream."
In some (American) circles, "creamer," is of the dry-powder variety, which can vary from the dry version of fresh creamer to simply powdered milk of some variety. It is sometimes sweetened and often not made of any ingredient that began its life as cow milk. In any case, if all I had was powdered creamer, I may offer it to you but only with significant disclaimers.
I do not frequent Starbucks or any other coffee shop. Perhaps someone who does, or someone who works at one, can shed some light as to their corporate standards for this. There are may Americans who consider what Starbucks does to be both the original and definitive way of serving coffee.
