These two games share a hub because they share a buyer and a room. Both are played standing, both are loud, both end up in a basement or a garage, and both have exactly one specification that decides whether the purchase works.
A regulation-size foosball table cabinet is around 56 inches long and 30 inches wide. That is the number in the listing. It is not the number you need, because on a through-rod table the rods slide out past the cabinet when a player pulls back - commonly 12 to 15 inches on each side at full extension, and more on the longest rods.
So a through-rod table in a 56 by 30 inch cabinet actually needs about 56 inches by 5 feet of floor, plus somewhere for the two players to stand. Push one side against a wall and half the rods stop moving. This is the single most common foosball buying mistake and it is entirely avoidable.
Telescoping rods solve it. A telescoping rod is hollow and the inner section retracts inside the outer one, so nothing projects past the cabinet. Telescoping tables can sit close to a wall, they are safer around small children, and they are the obvious answer in a tight room. The trade is feel: through rods are what competition tables use, and serious players prefer them.
Air hockey: the blower is the whole product
An air hockey table's playing character comes from how much air it pushes through the playfield. A 12-volt blower - the standard in family tables - moves enough air for a fun game and runs quietly. A 120-volt blower, which is what arcade tables use, moves far more, and the puck genuinely floats rather than skates. The difference is immediately obvious to anyone who has played in an arcade.
You can read the spec directly: look for the voltage and, where listed, the CFM figure. Most home tables under 6 feet run a 12-volt motor. Tables at 7 feet and up often step to 120 volts. If a listing does not state the blower voltage at all, assume 12 volts.
Size then follows: 5-foot tables are family tables for a spare room, 6.5 to 7.5-foot tables are what a dedicated game room should be looking at, and 8-foot is arcade. Add 2 feet of standing room at each end - players lunge - and 1 foot either side.
Honest advice about combo tables
Combination tables that promise foosball, air hockey, table tennis and pool in one frame are the most-returned product in this category. Each game gets a compromised version of itself: the air hockey blower is undersized because the cabinet also has to be a pool table, the pool cushions are shallow because the frame also has to carry rods. If you have the space for one good table, buy one good table. If you genuinely do not, buy the combo knowing exactly what the trade is.