Usually in the US (at mostly fast food chains) when we say two or three, we are referring to the sachet packed milk. If you are in a restaurant, where the sachets would look not so fancy, you'd say some milk. So you'd say two or three milk/sugar.
But in the UK, a milk is a more common thing to go along (especially with tea) compared to the US where we like to have our coffee without milk/cream mostly(and you might surprise people here if you have milk in your tea). Just a fact! dont know if it helps the context.