There are three types of route middleware in Nuxt.
Route Middleware

What is the difference between serverMiddleware and Route Middleware?

serverMiddleware runs on server-side for each http requests, while route middleware are called in before rendering a page.

Read more about serverMiddleware https://nuxtjs.org/api/configuration-servermiddleware#the-servermiddleware-property

https://nuxtjs.org/api/configuration-servermiddleware#servermiddleware-vs-middleware-

https://nuxtjs.org/api/configuration-servermiddleware#custom-server-middleware