The server admin has access to the server infrastructure. They can access the database directly, modify the code that runs lemmy, turn off the site, often has control of the domain name and makes sure it points to the server, etc. The server admin has control over the software that runs the instance and the computer it runs on. They might have an admin account too, but that is not strictly necessary.

With “site admin” I assume that you mean someone with an account that has admin privileges. Such an administrator can access the instance with an account that can see and take action on instance-wide reports, can modify the site’s side bars, create emojis, and has other admin privileges. These admin privileges live within the website itself and are determined by lemmy’s code. This admin does not automatically have access to the server nor the database.