App Engine is a Platform-as-a-Service. It means that you simply deploy your code, and the platform does everything else for you. For example, if your app becomes very successful, App Engine will automatically create more instances to handle the increased volume.
Read more about App Engine
Compute Engine is an Infrastructure-as-a-Service. You have to create and configure your own virtual machine instances. It gives you more flexibility and generally costs much less than App Engine. The drawback is that you have to manage your app and virtual machines yourself.
Read more about Compute Engine
You can mix both App Engine and Compute Engine, if necessary. They both work well with the other parts of the Google Cloud Platform.
EDIT (May 2016):
One more important distinction: projects running on App Engine can scale down to zero instances if no requests are coming in. This is extremely useful at the development stage as you can go for weeks without going over the generous free quota of instance-hours. Flexible runtime (i.e. "managed VMs") require at least one instance to run constantly.
EDIT (April 2017):
Cloud Functions (currently in beta) is the next level up from App Engine in terms of abstraction - no instances! It allows developers to deploy bite-size pieces of code that execute in response to different events, which may include HTTP requests, changes in Cloud Storage, etc.
The biggest difference with App Engine is that functions are priced per 100 milliseconds, while App Engine's instances shut down only after 15 minutes of inactivity. Another advantage is that Cloud Functions execute immediately, while a call to App Engine may require a new instance - and cold-starting a new instance may take a few seconds or longer (depending on runtime and your code).
This makes Cloud Functions ideal for (a) rare calls - no need to keep an instance live just in case something happens, (b) rapidly changing loads where instances are often spinning and shutting down, and possibly more use cases.
Read more about Cloud Functions
Answer from Andrei Volgin on Stack OverflowApp Engine is a Platform-as-a-Service. It means that you simply deploy your code, and the platform does everything else for you. For example, if your app becomes very successful, App Engine will automatically create more instances to handle the increased volume.
Read more about App Engine
Compute Engine is an Infrastructure-as-a-Service. You have to create and configure your own virtual machine instances. It gives you more flexibility and generally costs much less than App Engine. The drawback is that you have to manage your app and virtual machines yourself.
Read more about Compute Engine
You can mix both App Engine and Compute Engine, if necessary. They both work well with the other parts of the Google Cloud Platform.
EDIT (May 2016):
One more important distinction: projects running on App Engine can scale down to zero instances if no requests are coming in. This is extremely useful at the development stage as you can go for weeks without going over the generous free quota of instance-hours. Flexible runtime (i.e. "managed VMs") require at least one instance to run constantly.
EDIT (April 2017):
Cloud Functions (currently in beta) is the next level up from App Engine in terms of abstraction - no instances! It allows developers to deploy bite-size pieces of code that execute in response to different events, which may include HTTP requests, changes in Cloud Storage, etc.
The biggest difference with App Engine is that functions are priced per 100 milliseconds, while App Engine's instances shut down only after 15 minutes of inactivity. Another advantage is that Cloud Functions execute immediately, while a call to App Engine may require a new instance - and cold-starting a new instance may take a few seconds or longer (depending on runtime and your code).
This makes Cloud Functions ideal for (a) rare calls - no need to keep an instance live just in case something happens, (b) rapidly changing loads where instances are often spinning and shutting down, and possibly more use cases.
Read more about Cloud Functions
Basic difference is that Google App Engine (GAE) is a Platform as a Service (PaaS) whereas Google Compute Engine (GCE) is an Infrastructure as a Service (IaaS).
To run your application in GAE you just need to write your code and deploy it into GAE, no other headache. Since GAE is fully scalable, it will automatically acquire more instances in case the traffic goes higher and decrease the instances when traffic decreases. You will be charged for the resources you really use, I mean, you will be billed for the Instance-Hours, Transferred Data, Storage etc your app really used. But the restriction is, you can create your application in only Python, PHP, Java, NodeJS, .NET, Ruby and **Go.
On the other hand, GCE provides you full infrastructure in the form of Virtual Machine. You have complete control over those VMs' environment and runtime as you can write or install any program there. Actually GCE is the way to use Google Data Centers virtually. In GCE you have to manually configure your infrastructure to handle scalability by using Load Balancer.
Both GAE and GCE are part of Google Cloud Platform.
Update: In March 2014 Google announced a new service under App Engine named Managed Virtual Machine. Managed VMs offers app engine applications a bit more flexibility over app platform, CPU and memory options. Like GCE you can create a custom runtime environment in these VMs for app engine application. Actually Managed VMs of App Engine blurs the frontier between IAAS and PAAS to some extent.
Hi, I'm studying Google Cloud because I want to work in it in a near future but I have a problem to understand the advantages to use a Compute Engine over an App Engine. If I have understood, App Engine is a solution to deploy web applications where Computer Engine is more a virtual machine that need some customization/maintenance by the developer (or similar professional people).
My question is: because I want use the cloud also to have a standard solution in the infrastructure managed by other people (so, I have no costs in resources in maintenance), in which situation I should prefer a Compute Engine over an App Engine? The first response is that a Compute Engine is more useful in not-web applications like batch or database, but Google cloud already offer specialized solutions respectively in Batch (managed service) and Cloud Spanner ( or Datastore or Cloud SQL).
Do you have sometimes choose a Compute Engine despite the configuration of the VM at your charge?
App engine standard vs cloud run use cases
Google Cloud Run vs App Engine for a monolith API
Reddit
Is Cloud Run a replacement for App Engine Flexible Environment?
The main difference is Cloud Run only executes when there is a live request on the wire, i.e. you are actually serving an HTTP request. As soon as the last socket closes/the last client disconnects, your container hibernates and does virtually no background processing what-so-ever.
If you're only ever doing work based on an HTTP request, then Cloud Run is definitely the way to go. Otherwise, if you have background tasks that run internally, you'll want to stick with AEF.
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