It's different today though. While the historically famous Edo period lasted 265 years, today the periods just end when an emperors reign ends. They are also counting years (today, not sure if they did earlier). E.g. 2018 is 平成30年 (Heisei year 30).
You're mixing up eras and reigns. The "Edo period" refers to the years when the shogunate ruled from Edo (today's Tokyo), during which there were over a dozen (notionally) reigning emperors:
