differentiate between barrel/stroke and barrel/cycle?

Answer 1

If this question is about reciprocating pumps, barrels/stroke refers to the volume displacement for a single unidirectional movement of the piston while barrels/cycle refers to displacement for a full cycle of two strokes. See the ref. and especially note that for double-acting pumps (pumps that deliver on each stroke) there is twice the displacement per cycle as per stroke.