At 250 rep as well as being able to view open and close votes on your own questions you can also cast open and close votes. These have the same weight as votes from other users - i.e. 1 of 5 - so your name will appear along side all the other voters.
However, if you agree with the Community when they have cast close votes and flags that it treated as a binding close vote but it's assigned to Community.
What I'm guessing happened here is that the OP saw the close votes, agreed and cast their own (which may well not have been a duplicate vote). They then saw the Community raised message and clicked on that to complete the close process.
In your second example the user has less than 250 rep so would only have ever seen the Community generated message.