The time periods in the correct order from LONGEST to SHORTEST are Era, period, and stage.
An era is a period of hundreds of millions of years and it is independent of human activity. For example the pre-colonial era, the cold war era, agrarian era.
A period is the basic unit of time. A Period lasts tens of millions of years. Normally we say that someone has lived for a period of time be it short or long.
The stage is a point in time when something happened. Children mature in stages, the same as animals and other creatures. This shows the time things are happening.
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