Definitely not the same.
I know it's subtle, but self-reliant is more about the team diving approach, diving with others and being able to be alone occasionally.
Solo diver is exactly that: from planning, config, setup, loading up, checking kit and the dive, it's all alone. The in-water time is an assessment of the skills you've brought along, aside from trivial coaching, you must be able to safely cope with all failures, whatever are thrown at you (blindfold, tied up, air-gunned, fin removed and a blindfold ascent with stop....)
This is why the Self-Reliant Diver card is pointless. Certainly in the UK it's not accepted anywhere for solo diving. Only the SDI Solo Diver certification is accepted.
I've personally nothing against self-reliant divers. It's important to know what it's about. But it's not the same as a solo diver. Worse still, from my PADI days, the self-reliant "course" was frequently mentioned as being equivalent, which it isn't.
How would you all describe the differences between the "courses"?