A regime is the leader and other people who run a government of a sovereign state.
There are many kinds of regimes. They can achieve power in many ways. Depending on the time and place and local civics like the electoral system, they can lose power in many ways too. The most common way for a regime to lose power was a coup, invasion or revolution until the 20th century. After that it became very dangerous and difficult to use these methods. Peaceful regime change is usually by an election - this method is now used by more than half the people on the Earth. It is called representative democracy. Such regimes are often called administrations to make it clear they are not dictators, and since the executive branch does not have all the power itself - it may share it with a legislative branch. Also the judicial branch is separate. The courts are not usually considered part of the regime.
However, some things are the same no matter how the regime achieved power:
When many regimes negotiate at the United Nations or World Trade Organization, it does not matter at all how each regime got its power. It matters only that they can agree and make everyone in their country do as the agreement says.
When someone wants a regime to change in another country, they usually are not able to do this by any means other than violence or interfering in its election. This is common if a regime is threatened by another regime.
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