AFAIK, this vote is on confidence in May as PM — that's quite different from a vote of confidence in the government. That would also involve Opposition MP’s; and, if successful, would likely trigger an election. (Very likely; but not certain, as the Queen decides.)
Britain, and other nations of the Realm, don't have a Chief Executive, who stands apart from the legislative branch. The PM is a member of Parliament, and is considered to be “first among equals”.
good info, thx!!