My hosting company offers up to 6 websites hosted for the one low price. I created a website which is ranking very well and have now created a second site (unrelated in topic) to the first site on the same hosting plan. I now realize this second website is considered a sub-domain of the first website according to my CPanel, although they have completely different domain names. Will this 2nd site be considered of lesser importance by the search engines or is this whole sub-domain thing just visible to me in my CPanel? Should I move the 2nd site to a separate new hosting plan

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You might be confusing subdomain with the folder structure of your website.

A subdomain is a name that comes before your domain name. In the case of www.google.com there’s also images.google.com, maps.google.com, etc. Each of these are websites in their own right, but their names share the domain name. Search engines see these as their own website. Subdomains are a handy way to organize a logical “entity” of a website.

The folder structure is how the websites are organized on your web hosting server. If your package provides 6 websites, then it’s probable that each domain’s files & folders are kept in a single domain folder (which in turn, is kept in a folder for you, the hosting user). At the “top level” of your web hosting folder, you’d have a different folder for each domain.

The cpanel allows you to map a folder to a (sub)domain.

You DO want your different (unrelated) websites to have different domain names as a start of your “branding”.