When running code in Anaconda or IBM Watson Studio, is Anaconda and IBM Watson Studio using your local device’s RAM or are they running the code in the “cloud” servers?
It depends. Watson Studio Desktop uses the resources of your computer, and also an Anaconda installation on your computer.
Watson Studio on Cloud (dataplatform.cloud.ibm.com) runs your code in the IBM Cloud. The browser renders the result on your screen, using your computer's resources only for that.
Watson Studio Local can be installed by others in their data centers. Then your code would be running in that data center.
If you have installed Anaconda locally on your computer, your code will typically run on your computer. Unless you explicitly write code that sends requests elsewhere, for example to call Watson APIs in the cloud.