Spectre2 should allow malicious JavaScript to read data from other processes.
Running browser tabs in separate processes (e.g. Google Chrome's new Site Isolation) should protect data from Spectre1 alone but not Spectre2.
See the table here:
https://security.googleblog.com/2018/01/more-details-about-m...
If that's not right I'd love to be corrected.
Probably no known exploit of this yet.