Sometimes on the killboards, there's an icon like this:
Normally the background isn't red:
What does red mean?
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Sign up to join this communitySometimes on the killboards, there's an icon like this:
Normally the background isn't red:
What does red mean?
If the background is red, it means that the weapon killed the player with a crit.
So in your first screenshot, it could be read as:
soccer sam88
Phlogistinator (crit)killed Table
whereas the second screenshot would read as:
didn't notice you
Ubersaw (noncrit)Neil Armstrong
As an additional note, as mentioned by users in the comments, the background for mini-crits looks exactly the same as if you had killed the player with the critical hit.