It think your question was not about the internal hierarchical routing and IP prefixes, than much more about the techniques itself - right? Well, some savage once thought that the IP addresses don't tell you everything (true) so he came up with the idea of logging the DNS questions and answers - passive DNS. This way the ISP has the mapping between the names you type combined with the IP addresses so that DNS requests provide a much better overview - but they do not the know the full URL, which is on the HTTP level. However they have the port numbers and protocols being used. So now they filter services. When you visit a specific website, it contains specific plugins, ads, trackers, etc which all reveal DNS requests. Any ISP who wants to grow does this mainly for accounting hush..dig...profile...hush. The DNS method does not show the full URL but it has no overhead data in the packets and it's amazingly efficient to build up a digital fingerprint.
I mentioned the HTTP level - the same data can be gained if your ISP is monitoring your HTTPS traffic. They will see
www.stackexchange.com but the rest is not visible because the (clean, no MITM, operating on a smaller scale) certificate is registered to domain.com. However your ISP could MitM your connection to utterly and completely defeat the encryption, and you would never know. HTTP is plain text, unlimited raw information - which gives ALL POWER to your ISP or someone who is monitoring your traffic. This is a lot of data, but you can assume your ISP has a tool which does a deep packet inspection on the Socket API level - so they don't have to store the full packets.
In theory if you want to obfuscate such monitoring you would connect to a rooted server or a strong VPN (L2TP/IPsec, no logs) then use Tor (Tails) and all encrypted services - this way all your ISP would see is undecipherable gibberish, well they would see an enstablished connection to the VPN (which would then see you are connecting to tor). And they would not care - unless its consistent extreme saturation of your line, especially if it impacts other users.
The answer to the question: No, they cannot click on your URL - they have to copy paste it. They certainly don't bother.