Larry,
As Hilmar has already said the fdifference between a validation rule and a trigger is when it is applied, triggers are done last after the validation rules and the index uniqueness rules have been passed.
A situation for using a record validation rule r=instead of a field validation rule is this ...
Employee table
Marital Status Field (must be Married or Single)
Spouse's Name (must be blank if Single and filed if married)
Try enforcing the above rules with field rules. The user cannot make the employee married because the spouse's name filed is blank and they cannot put in the spouse's name because the mnarital stauts is single. A close loop that the user can never get out of. The only way to apply this rule is to wait for all fields to be completed and then apply the rule. We can marital stauts to Married or Single using the Marital status field validation rule, but we cannot apply any rule that involves the spouse's name there.