The regulations draw a line based on aircraft seating. “Commuter” operations (which are scheduled operations) with a non-transport category turboprop with less than 20 seats or using a transport category turboprop or jet with less than 31 seats fall under 135. “On demand” operations are not defined but they also fall under 135 rules. So if it is a charter operation but not 121 Supplemental it would also be a 135 operation.
It used to be so simple, a DC-3 or smaller was 135 and larger than a Three was 121.