Agreed. There is a distinct difference. The only reason I posted this one is because they claim to take submissions of other people's work, even if it is by invitation only.
That is the big distinction. It's not a problem if self-published authors have their own imprints. All they can do is screw up their own books, which are their own property and their own look-out. It's when they solicit other writers' work, and undertake to publish it, that we take an interest in them.
Open submissions and submission by invitation only are both solicitation. They're asking to be granted the use of other authors' work.
A basic explanation for anyone who hasn't previously run into this pattern: it's a tipoff when a flaky new startup publishes books written by the founder and publisher. What it generally means is that that person didn't get into the business because they wanted to be a publisher; they did it because they wanted to get their own books published. It doesn't bode well for their competence, expertise, or long-term fortitude.