The rooting thing is a bit silly. Of course it's the same unless the definition of "same" is bizarre which happens a lot these days.

Seed can result in anything. But I've always gotten a tomato I couldn't tell apart each year. Did that for about 10 years with a cherry type tomato that sprouted from the garden soil in a new house and I went with it.

I don't think these 2 things differ for determinate or indeterminate. But I'm no expert.

If you root a cutting you are getting the exact same type of plant. Not sure where you read it wouldn't be but nothing could be further from the truth. As for the seeds, assuming you are growing an open pollinated variety and they weren't cross pollinated, then you will get the same type of plant from them.

Rodney

Ok so what if the determinate tomato is already done growing, will I get fruit from the rooted cutting?

Possibly. I haven't tried it with a mature determinate plant. Indeterminates would fruit for sure if there is enough time left in the growing season.

Rodney