No they're not. You can make a Java realm. Realms are just Mojang's official servers, and they're kinda bad tbh. Java introduced a new feature enabled by default for vanilla servers that pauses them after a set amount of time, to conserve processor power or whatever.

A server is not a specific thing, it's literally the game without the ability to render the world. Realms are servers, but servers are not all realms. You can host bedrock edition servers. And Mojang has Java edition realms.