No, they’re different.
On American, Main Plus is basically a standard Main Cabin ticket with some extras bundled in, like one free checked bag and seat selection benefits. You’re still sitting in regular economy.
Premium Economy is a completely separate cabin, mostly on international long haul flights. It has bigger seats, more legroom, upgraded service, and different baggage rules.
For domestic flights, you usually won’t see a true Premium Economy cabin. That’s probably why the baggage chart looks confusing.
If you booked Main Plus domestically, you’ll get the one free checked bag included. The “0” under Premium Economy is referring to that different cabin product, not Main Plus.