Why is a the price different for the same train at the same time, same destination, on different websites? I looked at Trainline but the same train is a different (lower) fare on sncf- connect? ? And another train website showed another fare. Thank you

Because there is only one company that actually runs the trains, the official french railway, SNCF, the others are for profit resellers. They are not charities and want to make a profit, of course, or they would have no reason to exist.

AFIK, every vendor should sell at the same price, including SNCF Connect. Did you complete the booking process to get an actual quote? Because SNCF charges a hefty cost for real time access to inventory and most vendors will rely on previous requests to display the 1st screen with prices that are not updated.

With the dynamic pricing just like the airlines, the cost of main line SNCF tickets can vary every day, even if you just use one website.

I kept searching and found this site, https://www.seat61.com/France.htm It explained the various seller options. I think I will go with the SNCF site. Thank you.

SNCF sell very few tickets. The main vendor is SNCF Connect, a subsidiary that has signed the very same distribution agreement with SNCF as the others like Trainline for example: same constraints, same compensation for sales.
Vendors make their money with distribution fees paid by SNCF, based on volume. Not on the fare charged to end customers. This would be a breach on contract.
SNCF is a train operator, not a vendor. The airline model is different: most airlines also distribute their product

kerouac's and rouelan's comments are correct. And Mark, the Man in Seat 61 is always a good go-to place for detailed information about specific trains.

You should get the SNCF Connect app and use it. to search routes, timetables, and possible disruption of trains (i.e. track works). And purchase and download tickets to your wallet. Everything is mobile these days, although for now you can still print your tickets