To dovetail from what @kimera said, if you look at the some of the words provided for period and interval in a 国語 dictionary, you’re going to find some differences with regard to overlapping meanings and such. Let’s look at the definitions of 時期, 期間, 時代, and 間. (Rather than posting some of the lengthy definitions, I’m going to paraphrase them in English for the sake of time). Also, for clarity, I when I use Interval or period they are in reference to the definitions provided in the Merriam-Webster dictionary.
時期 - This word carries the meaning of 期間 and season within it, but also includes the meaning of carrying out something in a specified time. Also a certain demarcated period of time. Which carries the meaning of period (according to MW dictionary’s first definition)
期間 - This word had the shortest definition, essentially stating the period from one determined thing to the next determined thing. This is similar to interval, This carries a little of both interval and period’s meanings.
時代 - This carries the meaning of historical periods as well as past and present periods of time. This meaning overlaps well with one aspect of the English word , period.
間 - This word had the most definitions as that it’s a more generic word. This word encompasses the idea of temporal and spatial distance along with other specific uses which I won’t mention.
Although the overlap makes doing reviews a pain, the actual use of Japanese language is going to need a deeper understanding so one doesn’t misunderstand or misuse these words.