Regular Elliptic Curve Diffe Hellman vs Curve25519 (X25519) diffe hellman

As the post says, im struggling to understand the difference between the regular and x25519 diffe hellman functions. For an assignment i need to produce a lightweight crytpographic system that encrypts with a symmetric Cipher and then encrypts that key with an asymmetric cipher, i elected to use ECC for this but i'm really struggling to understand the key exchange. I understand that i need to obtain the recipients public key via their digital certificate but from there i don't understand how to derive a key to encrypt the chacha20 key with chacha20. I was told using curve25519 was the most performant but then i've found out that it has a more complicated process of key exchange and key derivation. Could someone explain this to me? Thanks in advance for being patient with me, i'm still quite new to this