They are very different.
In Play 2.3.x and prior, play.core.Execution.Implicits.internalContext is a ForkJoinPool with fixed constraints on size, used internally by Play. You should never use it for your application code. From the docs:
Play Internal Thread Pool – This is used internally by Play. No application code should ever be executed by a thread in this thread pool, and no blocking should ever be done in this thread pool. Its size can be configured by setting internal-threadpool-size in application.conf, and it defaults to the number of available processors.
Instead, you would use play.api.libs.concurrent.Execution.Implicits.defaultContext, which uses an ActorSystem.
In 2.4.x, they both use the same ActorSystem. This means that Akka will distribute work among its own pool of threads, but in a way that is invisible to you (other than configuration). Several Akka actors can share the same thread.
scala.concurrent.ExecutionContext.Implicits.global is an ExecutionContext defined in the Scala standard library. It is a special ForkJoinPool that using the blocking method to handle potentially blocking code in order to spawn new threads in the pool. You really shouldn’t use this in a Play application, as Play will have no control over it. It also has the potential to spawn a lot of threads and use a ton of memory, if you’re not careful.
I’ve written more about scala.concurrent.ExecutionContext.Implicits.global in this answer.