In the USA, we pretty much decided long ago that our machines would just take a single kind of coin (usually quarters), and we set the games to require X coins for a game, and that's how the pricing is determined. We also often have bill acceptors (since dollar coins are not in widespread usage) that hook up to the game board via a separate input, and the game knows that the value is different and will award you the appropriate amount of credit. Most bill acceptors can also be programmed to output the appropriate number of "coin pulses" (e.g. 4 for a dollar bill) to simulate the player putting in 4 coins if the game doesn't support bill acceptors directly.
In many other countries, the use of other size coins is more widespread, so "credit boards" are common along with a more complicated coin mechanisms. Rather than simply passing coins of a certain type to a switch and rejecting all other coins, these coin mechs determine what kind of coin was inserted and signal some electronics to output a number of pulses that varies with the kind of coin. E.g. putting in a 10 cent coin would give you one credit (by pulsing the coin signal once) but a 1 dollar coin would give 10 credits (by pulsing the coin signal 10 times). This is more complicated and prone to failure than the single coin only system, which is probably why it's only used where lots of different coins are common. I'd say this is probably way more complicated (and expensive) than can be justified for a home system, too.