CURVE is a payment system.
CURVE is an evolution of Bitcoin core.
Curve used, at launch in 2020, a non widespread algo, core intensive and not very power consuming.
POW started on CPU and for 2 years GPU's were out of game, later in 2022 other coins were launched who adopted this specific algo, all forks from CURVE or PPC had an issue on POS blocks refused by network, CURVEhash with huge help from the community managed to solve the issue, so you can mine, buy and stake CURVE.
Planning hadfork to introduce mandatory fixes as update in mid/late-2002.
Curve25519 is a state-of-the-art Diffie-Hellman function suitable for a wide variety of applications, you can find more info on https://curvehashcoin.com