RequiredFieldValidator is to validate the mandatory fields. So for all the fields that are mandatory you will have to put a
RequiredFieldValidator.
RegualrExpressionValidator is for checking the input. you can use regular expression to accept only valid inputs and save yourself from checking the inputs serverside. For all the controls that need some specific type of input like number only or alphanumeric only you will have to use this.
Now if any control is mandatory and need specific input type you will have to use both. Refer this for details:
Understanding ASP.NET Validation Techniques[
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