RingCT: hidden amounts
Every amount on Coin is sealed. The network still checks that no coins were made out of thin air, without ever seeing a single number.
Automatic. Every amount in every payment is sealed. There is nothing to turn on.
Anyone can check both facts. Nobody but the sender and the receiver learns the amounts.
Amounts become commitments
Each amount is replaced with a Pedersen commitment: a sealed value that hides the number, yet can still be added and subtracted like one.
The sums still have to match
The network adds up the sealed inputs and the sealed outputs, plus the public fee, and checks that they balance. If anyone tried to send more than they had, the sums wouldn't match and every node would reject the payment.
No negative amounts
Sums alone aren't enough: a sealed negative amount could balance a sealed amount that's too large. So each output comes with a Bulletproofs+ range proof, which shows the amount is positive and in range without revealing it. The proofs are compact and quick to check.
What stays public
Two things: the fee each payment pays, and the reward in each new block. Both are public so anyone can check the total supply of Coin for themselves.
Who sees the amount
You, and the person you pay. Their wallet unseals the amount meant for them, and yours keeps track of your change. Nobody else does, unless you choose to show them with a payment proof or a view key.