In Kotlin, what's the difference between the terms Coroutine and Continuation?

It's true, these two are quite closely related. To resume a coroutine, you actually call continuation.resume().

Each coroutine has its associated continuation object. Actually, you don't need anything else but that object, it contains the complete state of the coroutine.

To a certain degree, Kotlin uses "coroutine" to also include the coroutine context, which gives the coroutine the knowledge how exactly to suspend itself, where to keep the continuation while suspended, and how to resume (dispatch) it later. But you can also use the Unconfined coroutine context, which is almost as good as no context at all, and be in total control of resumption with nothing but the continuation object being preserved:

import kotlinx.coroutines.Dispatchers
import kotlinx.coroutines.GlobalScope
import kotlinx.coroutines.launch
import kotlin.coroutines.Continuation
import kotlin.coroutines.resume
import kotlin.coroutines.suspendCoroutine

var continuation: Continuation<Unit>? = null

fun main(args: Array<String>) {
    GlobalScope.launch(Dispatchers.Unconfined) {
        println("Suspending")
        suspendCoroutine<Unit> { cont ->
            continuation = cont
        }
        println("Resumed!")
    }
    println("After launch")
    continuation!!.resume(Unit)
    println("After continuation.resume(Unit)")
}

Here you can see that we reproduced the whole suspend-resume scenario while keeping nothing but the Continuation object.

My conclusion is that, due to the features of Kotlin's coroutine design (especialy the fact that they are stackless), there's a blurry line between the concepts of "coroutine" and "continuation".

Coroutines are procedures that take turns doing their task and then suspend to give control to the other coroutines in the group, and resume task.

Continuation is the stack that controls the flow of the program, that allows it to skip into different parts of your program. You could use it to control the flow including coroutine like a global switch.