Could someone help me out with interpreting the luggage rule on bringing luggage on train? I am traveling with family and will have mid-sized, airline checked-in luggage. I don't think they will fit the overhead compartment.

JR seems to say that passengers who want to bring travel size luggage need to purchase reserved tickets, which costs more. But here is the issue. Train carts seem to be separated into reserved and non-reserved. Which means, even though I only have 2 luggage, in order to seat with my family. I need to buy reserved ticket for each family members. Unlike airlines which I just pay for the luggage. Is my understanding correct?