tl;dr: (1) a subdomain is part of a domain, (2) other domains can point to the same server, (3) people could see through that if they wanted to
By definition, a subdomain is part of a parent domain
If you have a subdomain
abc.example.com, that is necessarily part of
example.com relationally speaking.
Separate sites can be hosted by the same server
As explained in the QA you linked, you can have DNS point a site at another. Say you set up the domains/subdomains:
You and your friend could then get other domains, eg
user9570789spoliticalblog.com and point them at those subdomains.
With a bit of configuration (eg if using Wordpress, set the site URL as
blog.example.com) things should Just Work™. Configuration is way beyond the scope of this article*, however.
If you want to truly separate them, this way of doing things is only 'skin deep'
If set up as above, then at a quick glance all parts will be completely unconnected.
However, if you absolutely need to keep them separate -- let's say your blog has unpopular political views, or your friends gaming community is controversial for whatever reason -- then you should take steps to keep them so.
Depending on how it is set up, a DNS query (not normally seen by end users but trivial for someone to do) may say something akin to "The record for
joebloggsgameserverforum.com points to
forum.example.com". Or it may just say "The IP for
188.8.131.52". There are ways to find out what else is being served from a particular IP, and someone may find out "
example.com"; and that might not be something that you want.
This would almost certainly be a problem if you are a political dissident hosting (or even writing!) a blog criticising a repressive regime -- people have literally been imprisoned for that -- or if your friend's 'gaming community' is Anonymous or something equally controversial. Or you may be happy keeping them superficially separate because one just doesn't have much to do with the other!
The security and separation aspects are also beyond the scope of this question- the above will keep them 'separate'; but you have to pay attention to how separate "separate" is to you.
*:Configuration problems may be on-topic here or another SE, or may have already been asked! There's lots of help around and on offer.