You have 2 questions here.
The first one:
- What are the difference with local development of SFDX https://developer.salesforce.com/blogs/2019/10/announcing-lwc-local-development-beta.html ?
This is from the documentation (emphasis mine):
Local Development enables you to build, run, and test your Lightning Web Components without deploying your code to your Salesforce org.
As it mentions, you don't need a Salesforce Org to be able to validate the components you are building but can do so on a local server.
The other part of your question is as:
To summarize my main confusion is between this 2 websites:
For the difference between these two, at a very high level:
Salesforce DX (SFDX) is targeted to build & deploy components directly in a Salesforce Environment. So you will create a component locally, deploy it to a Salesforce sandbox and be able to test that out using this.
Salesforce Developer Experience (DX) is a new way to manage and develop apps on the Lightning Platform across their entire life cycle. It brings together the best of the Lightning Platform to enable source-driven development, team collaboration with governance, and new levels of agility for custom app development on Salesforce.
On the other hand, LWC Open Source is different that Local Development. LWC Open Source is an Open Sourced version the Salesforce Lightning Web Components framework which allows one to be able to build & deploy locally or any platform other than Salesforce. Below is the excerpt from the docs:
Build apps anywhere, any way. You can build an app with your favorite tools, like Webpack, TypeScript, and Babel, and run it on Heroku, Google, or anywhere else. You can also package an app to create a desktop experience in Electron.