What is the difference between https://sandbox.paypal.com and https://developer.paypal.com ?
I mean: I need to generate API credentials to make some tests on SOAP API for Express Checkout and I can't understand if I need to use my developer account or I need to create a new Sandbox account...
Which one I need to use to test my application?
The Sandbox is the correct place to test your application. Basically you can say: "sandbox.paypal.com" is the test network of PayPal and "developer.paypal.com" is the control center for the live version and the sandbox version.
Read the official documentation >here< if you want to know how to get started with the PayPal Sandbox.
You need to use your REAL PayPal Account for the Dev Portal. In the Dev Portal you create TEST Accounts that you can use for your Sandbox. In the Dev Portal you can also create the API Keys. How you do this is explained in the Link that I mentioned.