On the 2-6-0 without a tender: This is a "tank" loco. The water was carried in those tanks each side of the boiler, and the fuel, either wood or coal, was carried in the box behind the cab. This has the look of a (pre-electric) suburban loco, although most of them had a pilot and a headlamp at each end, so they could run in either direction without being turned at the end of the line. The very limited fuel supply also dictates short runs.
BillS