I'm new to IBM Cloud and cloud platforms in general and wanted to start my Flask app on IBM Cloud, I just started with this Getting started with Python but I'm very confused with how it will work.
Is Cloud Foundry working the same way as containers work?
How the platform handle the dependencies in order to Flask use them in both deployment ways?
Your question is (almost) too broad. I can give you some basic answers, but everything else should be separate questions when you run into specific problems. You are referring to the Getting Started with Python and Cloud Foundry on IBM Cloud (this is the IBM Cloud docs, not the GitHub repo).
When working with Cloud Foundry (CF), the CF environment and buildpack takes care of the dependencies. For Python, they are specified in the file requirements.txt and there is the file manifest.yml to configure the app, its name, memory usage, domain and more. When you push the app (either cf push or ibmcloud cf push) the two files are taken into account and everything else is done automatically. That's the appeal of Cloud Foundry.
With containers, you would write a Dockerfile, then build the container image, push the image to a container registry, deploy the container to Kubernetes. When you build the container, your script would need to take care of resolving the dependencies (based on requirements.txt) and include the necessary modules into the image.
I recommend reading the Deploy an Application Cloud Foundry doc as a starter to give some more background. There is also a simple IBM Cloud solution tutorial that walks you through the steps of deploying a Flask app with a Db2 database. That same site with IBM Cloud solution tutorials also has an overview of tutorials by deployment option (Cloud Foundry, Kubernetes, Cloud Functions, etc.).