Both or only the first, but never just the second

In the real example,

You should probably use javascript or jQuery to accomplish this

you can achieve the objective by reversing the order and adding a couple of words to emphasise the difference:

You should probably use jQuery or just plain JavaScript to accomplish this.

Thus jQuery implies JavaScript; you could have JavaScript without jQuery; or neither.

Converting comment to answer

Can/May I serve you some fish with or without chips?

UPDATE: Would of course have been lovely to have seen the original reason for the question since I have A LOT more experience with JavaScript/jQuery than fish&chips

Since JavaScript is built-in whatever device that could run jQuery, the sentence Andrew wrote, is understandable by anyone versed in the art.
jQuery is a JavaScript library so the or relates only to plain JavaScript or vanilla.js as some people like to call it now

Converting comment to answer:

You could phrase it this way:

"You can choose Y if you have X."
"If you have X, you can choose to get Y".

You could describe this process as an incremental choice. You are making a base choice (whether or not to use javascript) and then a choice about whether to add a supplement (whether or not to add jQuery to the use of javascript).

The implication is that you cannot make the second choice unless you affirmatively make the first choice.