The first one will generate a link automatically with no code (on lemmy v0.18 and above, not necessarily in apps - it doesn't seem to work in Jerboa currently). This link is instance agnostic, meaning the viewer sees a link in their own instance, rather than the example.com instance. This means you can send them a DM, or open their comments and reply to them.

The second one isn't enough on its own, it needs to be in the form [link text](https://example.com/u/user). However, if you start typing @user@example.com on the website, a pop up box will allow you to select the user and generate the link code for you - it will give you [@user@example.com](https://example.com/u/user). This version is not agnostic, it takes you to the user's instance, however it does send a mention to the user's inbox.

Hopefully in a future update they will combine these two, so that an agnostic link will also send a mention, and so the mention link will auto-generate and be agnostic. Right now, one is for linking to a profile you want to interact with, the other is for calling that person into the thread with a mention.

Edit: Just for a little more fun variation, it looks like Jerboa handles the @user@instance link as if it were instance agnostic. On the website it opens the user's instance.

Yeah I know. But we're on lemmy here, so it's good to know.

Mastodon might not do that sort of thing, and kbin is different again. Tbh I'm surprised you even got my last comment (although it seems like you got it late) as most of the time kbin and lemmy don't federate properly through threads. For example, I was unable to reply to you on my phone in Jerboa, and on the website it doesn't work unless I specifically select English as the language.