So the UK is probably the simplest to discuss because it doesn't have a constitution, and this means parliament is sovereign and decides everything by a simple majority vote.
They can pass laws saying that certain things need a super majority, but then they can just turn round and unpass them as well
This means that what you think of as the executive, i.e. the prime minister and all his helpers, can be changed by a simple majority, and an election can be called by one. They don't need to happen at the same time. The last parliament had three different prime ministers without an election, and it's common to switch prime ministers well before an election in order to create an incumbent advantage.