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 @[email protected] 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 @[email protected]. 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.