Green Pass and reservations on smaller trains

I am planning on getting a Green JR Pass. However, I see that reservations are necessary on some of the big trains, but necessarily on the smaller, regional trains.

For example, if I were to travel from Kyoto to Nara, I don't see an option to upgrade to Green. In this case, I would imagine I would just hop on the train with my green pass.

Is that correct? What is the procedure for Green Pass holders on trains that don't have a green car? Also, is there an instance of any regional/local train which has a green section but doesn't require a reservation?

Thank you