After looking into how TLS handshaking works it seems to inherently include the Diffie Hellman algorithm during the point where they generate a shared secret key. However as I look into this some more I find articles such as this: https://thecybersecurityman.com/2018/04/25/https-the-tls-handshake-using-diffie-hellman-ephemeral/

"I published a blog post several months ago illustrating a simplified step-by-step process of how https and the TLS handshake typically work. BUT! There is an alternative approach that uses a key agreement protocol called Diffie-Hellman Ephemeral (DHE). This is a process of creating a secret key in plainsight using modular arithmetic."

Looking at the blog post mentioned it seems like the client uses the servers public key to create a shared private key and sends it back. So it looks like the burden of creating the shared key is actually on the client, and so this is different than Diffie Hellman. Is this correct? If so what are the pros and cons of using one or the other?