Situation : I am writing a chrome extension that works on any page.
Problem Question : I can not load jQuery into Facebook and I wo
You may know all of these by now, but I think someone still finds these useful.
In a Chrome extension,
You have some "worlds of scripts":
Google does a excellent job on documentation, so tons of document about all of those scripts https://developer.chrome.com/extensions.
But in your case, just note that: page scripts and content script live in separate worlds, they do share the DOM and some Chrome native objects, but they don't share variables (or objects) they create.
For this case, if you have jQuery in your content scripts, you will have $ and jQuery ready to use in your content scripts. You can use it to query the DOM (although some jQuery events may not work as expected). But on the page, you will not have $ and jQuery, (you might have $, but it is not jQuery ^^).
Your method 2 above, it actually injects jQuery into the page, that jQuery will become page script. And you cannot use $ or jQuery in your content scripts.
If you use both method at once, you can have jQuery 1 in your page scripts, and jQuery 2 in your content script, and they are 2 different jQuery instances. It might cause confusion, but I do it all the times.