[blibble]

it's the important detail

in the UK the electorate don't pick the leader

the electorate vote for an MP, and the group of those that form the party alone select the leader (and they can dismiss them just as easily)

the party has power over the leader, which is absolutely not true in most presidential systems

(and as to your second point, yes, under some hypothetical system that doesn't exist it's possible things may be different)