So this is a bit weird. Normally when we initiate a restart from within Firefox we set certain flags to ensure that the new instance uses the same profile as previously. It's these flags that I use to set the telemetry accordingly.
The restart buttons in about:profiles however does something different. It doesn't set the flags and so when Firefox restarts it will just go through normal profile selection again, so you can restart and end up using a different profile. That seems odd and not what I would expect from these buttons. I can't see any mention of why this is in bug 1179129. I'd like to propose that we "fix" this bug by just making these buttons do the normal thing and always restart into the same profile. What do you think Romain?
If we decide not to do that then I'd like to know what we should do in telemetry for this case.
Currently restarts of this kind will just generate one of the "firstrun-" or the "default" result. I could change it so for these restarts we get the "restart-" or the "restart" result but I'm not sure that that is correct since this seems like a different case. I can do pretty much whatever here easily, just need to know what is most useful to you Romain.