IMO 'epoca' is a long period of time, as in history or geology. 'Plazo" is shorter and more easily measured, as in rental agreements or business contracts.
Yeah, an epoch or an era in English.
What's the difference between el plazo and la epoca?
I think "época" is rather "epoch", "plazo" is "term"/"time-limit".
Why is "age" wrong?
Because it means time/epoch/period (in time)