Odds-on means the price implies better than an even chance: decimal below 2.00, fractional with the bigger number on the right (1/2). Odds-against is the opposite: decimal above 2.00, fractional 2/1 and up. Evens (2.00) is the border.
The vocabulary matters because psychology differs on each side. Odds-on favourites feel safe and are systematically over-backed by recreational money; odds-against underdogs feel like lottery tickets. Neither feeling has anything to do with value, which lives only in the gap between price and true probability.
1/2 fractional = 1.50 decimal = 66.7% implied: odds-on. 5/2 = 3.50 = 28.6% implied: odds-against. A 1.50 favourite that truly wins 60% of the time is a bad bet; a 3.50 outsider that wins a third of the time is a good one.