If you buy a 1,2 or 3 month pass, those are continuous passes and all travel days are in a row.

If you activate a one month pass on the 5th of June it is valid until the 4th of July.

If you buy a flexi pass, like 5 days in a month, you can use the travel days anytime during the month of activation.

If you are going to Germany this summer you might be interested in the 9 EUR ticket. It is not valid on ICE, IC or night trains, but on regional trains and on public transportation.

https://www.bahn.com/en/offers/regional/9-euro-ticket-en

What about the options where you just purchase any amount of travel days without a given time period to use them- the ones with the green calendar: can you use their travel days independently? 

(By the way: the website is in Dutch. ;-)

The pass for Germany is available with consecutive days and X days in 1 month:

https://www.interrail.eu/en/interrail-passes/german-rail-pass

the ones with the green calendar: can you use their travel days independently?

No, consecutive. Like in the green picture. 

thanks guys I just really wanted to not have any doubts ;-)