As far as I understand, due to license reqirements all web applications, which use MS SQL Server, use SQL Server Express (free) or SQL Server web edition (processor license).
Is it so?
What are other specific features of SQL Server usage for web app?
Essentially. You use a SQL Server Processor license when you don't want to have to buy Client Access Licenses.
A complete breakdown of the SQL Server Licensing schemes is here:
You can use any edition for web development.
You can start with 100% free express edition. Then upgrade to next level. The licensing is very flexible and the most you will need for web development is Standard edition.
SQL server allows you to use CALs only when you have identifiable users. When your connections are initiated from a public website where users don't log in, but browse anonymously, you're required to license SQL Server by processor, not by user.