ECDH can be used for public key encryption just like RSA can be used for public key encryption. However, the EC problem cannot be used directly to encrypt data like the RSA algorithm can be used.

Instead Diffie-Hellman is with a static key pair (similar to RSA) and an ephemeral key pair. The public key of the receiver can be used with the temporary private key to derive a symmetric key such as an AES key. This key can be used to encrypt the data. Then the data is send together with the temporary public key. Then this key can be used with the static private key to derive the same AES key, which finally can be used to decrypt the data. This way of using Diffie-Hellman key agreement to keep data confidential is called IES or ECIES when it is used with Elliptic Curve Cryptography.

So except for the method on how the symmetric key is established, the scheme is very similar to RSA encryption. And in both cases the security relies on a private key of a static key pair. Cracking either ECIES or RSA is considered very hard if the scheme is implemented correctly. Only a fully fledged quantum computer may break RSA or ECIES directly as neither scheme is secure against quantum analysis.

The parameters of the curve are always public. Leaking them does not let an adversary be able to calculate the private key nor the secret key calculated using the ephemeral key pair.

Note that there are some other models that use the hardness of the ECC problem to encrypt messages. But in general they similarly rely on a static key pair for the security of the scheme. ECIES is the most likely scheme to be used though.

ECDH can be used for public key encryption just like RSA can be used for public key encryption. However, the EC problem cannot be used directly to encrypt data like the RSA algorithm can be used.

Instead Diffie-Hellman is with a static key pair (similar to RSA) and an ephemeral key pair. The public key of the receiver can be used with the temporary private key to derive a symmetric key such as an AES key. This key can be used to encrypt the data. Then the data is send together with the temporary public key. Then this key can be used with the static private key to derive the same AES key, which finally can be used to decrypt the data. This way of using Diffie-Hellman key agreement to keep data confidential is called IES or ECIES when it is used with Elliptic Curve Cryptography.

So except for the method on how the symmetric key is established, the scheme is very similar to RSA encryption. And in both cases the security relies on a private key of a static key pair. Cracking either ECIES or RSA is considered very hard if the scheme is implemented correctly. Only a fully fledged quantum computer may break RSA or ECIES directly as neither scheme is secure against quantum analysis.

The parameters of the curve are always public. Leaking them does not let an adversary be able to calculate the private key nor the secret key calculated using the ephemeral key pair.

Note that there are some other models that use the hardness of the ECC problem to encrypt messages. But in general they similarly rely on a static key pair for the security of the scheme. ECIES is the most likely scheme to be used though.