Does it make a difference for SEO if I make my URLs like this:
mydomain.com/companies (main category exploration section)
mydomain.com/company/nike
As opposed to
mydomain.com/company (main category exploration section)
mydomain.com/company/nike
Does this matter for SEO?
There will be no difference for SEO to choose one or the other approach for your URLs.
However, I think it will be better to choose this schema because it seems logical to me:
mydomain.com/companies (main category explore section)
mydomain.com/companies/nike
Indeed, the category page refers to a list of companies and a detail page for Nike is just a presentation of one company belonging to all listed.
Moreover, with this approach, you can implement your website architecture without the URL problem of choosing a different one for each category page.
Your solution of
mydomain.com/companies (main category exploration section)
mydomain.com/company/nike
should be fine for SEO. If you like the way that the main cateroy URL reads with "companies", then go ahead and use that.
Users do occasionally try to navigate a directory structure. To support them, I would put in the following 301 redirects:
/company -> /companies
/companies/nike -> /company/nike