Most of the content available in a print library is purchased, and while it is still under copyright, the Law of First Sale permits the library to own it and loan it, and basically do anything but make and distribute more copies of it.
By contrast, online library content (that isn't free on the web) is always subject to license. It can be purchased, meaning that it is paid for once and available (theoretically) forever. Or it can be subscribed to, which means that it is paid for annually, and if the library stops that arrangement, the content goes away. But in both those cases, the content is hosted by the publisher or an intermediary called a vendor, and can only be used within limits that are set by the publisher and/or vendor.
This is why only faculty, staff, and students are permitted to access the content using their individual logins - if we allowed anyone else to access the content, we'd be voiding the license and lose access to the content. We might even be sued if we did it systematically. (Please never share your password!)
The license is also why in most cases, you are only allowed to link to the content where it "lives," and not save a copy and upload it to your online course, even though only faculty, staff, and students could ever access it there anyway. And it is why so many of our ebooks have severe limitations on downloading, converting to another file format, or printing. There are other limitations too, but they mostly affect activities that are internal to the library.