Salesforce Login URLs for Production and Sandbox are the following:

Production URL:

https://login.salesforce.com/

Sandbox URL:

https://test.salesforce.com/

To find out how Salesforce Login works, check the following:

How Salesforce Login works?

To brand your Salesforce Login Page, check the following:

How to brand Salesforce Login Page?

Salesforce My Domain is unique to your Orgs. So, know the Pros and Cons of Salesforce My Domain, please check the following:

Salesforce My Domain Pros and Cons