SharePoint sites vs. Site Collections - CONFUSED!

Your statement about sites meaning site collections is not correct. In that context, /sites/ is just part of the url address and is intended to provide a different path to a collection than the /teams/ path. MS came up with these 2 names when the stared O365 and since the words have very vague meanings they really don't provide much value.  Many companies will put certain type of collections in one or the other of these paths, but that is a totally arbitrary decision on their part (the MS Teams app does create new collections in the /teams/ path. )

You are asking an age old question that has existed since the early days of SharePoint 15 years ago :). It has to do with the fact that a site collection is really just a container of sites, when it is created, there is just one site in the collection (the top level or root) and this is created from a "site" template. To make it even more confusing, when you do this in code it is called a "web".  

It is theoretically possible to create each site/subsite in a collection from different templates, but this is typically a bad idea. 

Some of the site templates are intended to be the only site in the collection, but there is nothing that prevents you from adding subsites to them 

Community sites have been around for a long time and are totally different than Communication sites (which are new), see https://technet.microsoft.com/en-us/library/jj219805.aspx?f=255&MSPPError=-2147217396 for some info on Community sites.