When you order food it will mean what you suspect most of the time, a glass of juice ; this is so if the context in which the term is used clearly implies that a glass has been meant. However, it can also mean a particular type of juice; in this case you can sometimes also say "du jus d’orange".
In the food industry and in government agencies and other agencies in charge of controlling food standards, this will mean a particular type of juice very often, for instance a juice coming from Florida and subjected to a particular tax, or having a given content in vitamin C, etc.

For instance, someone who’d rather drink only orange juice from Florida might ask a question such as the following, although that is not likely to happen often in France.

• Je voudrais un/du jus d’orange qui vient de Floride ; en avez-vous ?

Another possibility, more likely that one, is this one.

• Nous voudrions un/du jus d’orange fraichement pressé, mais pas si ce sont des oranges du Maroc ; auriez-vous ça/cela ?

Yes, in the context of a restaurant or café, when you order something like, "Un jus d’orange, s’il vous plaît," or "Je voudrais un café," you mean a glass of orange juice or a cup of coffee. No need to say "un verre de jus d’orange." This construct is similar in English; when you say you’d like an iced tea, you don’t have to say a glass of iced tea.

It can depend on the drink; some are partitive, like de l’eau.

Jus is a substance, not a countable noun. When you use the determinant un (equivalent to English "a" or "one") or another number in front of a substance, it usually implies an amount. For juice or milk it would be a glass, for beer it could be a bottle or a pint, for coffee it would be a cup. This is a form of synecdoche, a figure of speech where the part implies the whole, or the container implies the content.

This sort of phrasing also exists in English: "You passed out after drinking a third glass." You didn’t drink glass, you drank a beverage served in a glass. It’s a simple shortcut we use to avoid saying either the substance or the container, whichever can be gathered from the context.

Note that you could ask for orange juice without taking that kind of shortcut.

• Je voudrais un verre de jus d’orange. I would like a glass of orange juice.
• Je voudrais un jus d’orange. I would like (an implied glass of) orange juice.
• Je voudrais du jus d’orange. I would like some orange juice.