Or can be used to mean:
- Logical or: A or B is true when A is true, B is true, or both are true and false when A and B are false.
- Exclusive or: A xor B is true when A is true, B is true, and no other cases.
For instance see here[1].
Either can be used in common speech. In law, there is often case law that argues for one over the other. This has been held as true in [patent law][2], where the xor variety can be assumed when the or logical operator is argued. Typically one writing a patent would rephrase to avoid the use of or entirely, although not everyone follows that advice.
The use of either can cause problems semantically. For instance:
Assume I like milk in my coffee is true.
Assume I like motor oil in my coffee is false.
Then I like milk or motor oil in my coffee by either definition above is true.
This, however, doesn't match common usage. In that common usage, or actually means and, because both paths must be true for the conclusion to follow.
The answer to your question is that either interpretation can be defended, or both, or neither, depending on context.
[1]: https://krissparks.medium.com/and-or-xor-bitwise-operators-2ae3fbcfa5bc#:~:text=Now%20the%20OR%20operator%20is,then%20the%20result%20is%20true.&text=Lastly%2C%20the%20XOR%20(exclusive%20OR,then%20the%20result%20is%20false. [2]: https://adamslaw.biz/2015/12/patent-claim-drafting-use-of-or/#:~:text=%E2%80%9COr%E2%80%9D%20may%20mean%3A%20A,Kustom%20Signals%2C%20Inc.