What settings are there for sending an email to the users who create accounts?
In configuration > people > account settings or going to config/people/accounts you can set who gets what and even modify the text

Register without admin approval

Check this setting

Who can register accounts? : visitors


and the user that registers will receive Welcome (no approval required) email which will include a one time link to complete registration.  Upon clicking on the link and following the instructions he is a registered user.

Register with admin approval

check the following setting 

Who can register accounts? : Visitors, but administrator approval is required


The user will get Admin (user awaiting approval) email upon registering and if enabled on Account activation the setting Notify user when account is activated is enabled the user will get a 2nd email upon admin approval.