I see these both in Bluemix, but what is the difference between them?

Cloud Foundry and OpenWhisk are two Bluemix Compute models that a developer can used to power an application's workload.

I'll give a very high-level summary of both services and when I would use them...

Cloud Foundry

• IBM Bluemix was originally based off Cloud Foundry's open technology. It is a cloud computing platform as a service that supports the full lifecycle, from initial development, through all testing stages, to deployment.
• Cloud Foundry has a CLI program called cf which is the primary tool to interact with Bluemix (or Bluemix provides a web GUI for this).
• Cloud Foundry introduces the concepts of Organizations that contain Spaces which you can think of as workspaces. Different spaces typically correspond to different lifecycle stages for an application.
• Cloud Foundry introduces the concepts of Services and Applications. A Cloud Foundry service usually performs a particular function (like a database service), and an application usually has services and their keys bound to it.

OpenWhisk

• OpenWhisk is a brand new IBM Cloud developed distributed event-driven compute model.
• It has a distributed automatically scaling serverless architecture that executes application logic on events.
• OpenWhisk also has a CLI program called wsk which can be used to run your code snippets, or actions, on OpenWhisk.
• OpenWhisk introduces the concepts of Triggers, Actions, and Rules.
• Triggers are a class of events emitted by event sources.
• Actions encapsulate the actual code to be executed which support multiple language bindings including Node.js, Swift and arbitrary binary programs encapsulated in Docker Containers. Actions invoke any part of an open ecosystem including existing Bluemix services for analytics, data, cognitive, or any other 3rd party service.
• Rules are an association between a trigger and an action.

Cloud Foundry vs. OpenWhisk

So the question remains: when should you use Cloud Foundry, or when should you use OpenWhisk?

In my limited experience using OpenWhisk, here are my thoughts. I like to think of OpenWhisk as an easily implementable automatically scaling architecture that application developers can use without needing much prior knowledge in backend development. I think of Cloud Foundry as a lower level in the software stack which might give you more customization, but will likely take more skill and knowledge for setting it up.

I would use Cloud Foundry if I...

• Was a backend & application developer.
• Had experience creating and connecting services together.
• Needed functionality that just might not be possible using OpenWhisk.

I would use OpenWhisk if I...

• Was an application developer.
• Didn't want to worry about a server.
• Didn't want to learn different programming languages, etc. to figure out how to set up my server.
• Really wanted focus on developing my application and have the backend just work.

Hope that helped.

Edit:

Here's a cool image that I found that illustrates this: