指定席 and 自由席: Assigned and unreserved seating
Compare a reserved-seat number on a ticket with a ticket for general seating. The distinction concerns seat assignment, rather than price or the number of available seats.
A specified or reserved seat
指定席 means a reserved seat. 「窓側の指定席を早めに予約した。」 reports booking a reserved window seat early. The location of the booked seat is stated.
「切符に書かれた指定席の番号を確認した。」 describes checking the reserved-seat number on a ticket. The number identifies the assigned seat.
Seating without an assigned seat
自由席 means unreserved or general seating. 「早めに並んで自由席の前方に座った。」 reports lining up early and sitting near the front of the unreserved seating area. It states where the speaker sat.
「この切符では指定席ではなく自由席を利用する。」 says this ticket is for general seating rather than a reserved seat. 自由 does not establish that admission is free or that seats are always available.
Read what the ticket specifies
Compare the 指定席 number with a ticket for 自由席 by checking whether a seat is assigned. Sitting near the front does not itself mean that the seat was reserved in advance.
Seat assignment, price, and available capacity are separate information. These examples explain seating arrangements without stating an exact fare or a number of available seats.
Is the distinction between a ticket with a 指定席 number and one for 自由席 about price or seat assignment?
Show the answer and why
It is about seat assignment. 指定席 identifies a reserved seat, while 自由席 concerns seating without an assigned seat. Neither price nor availability follows from that distinction alone.