If both controls the expression of another gene by physically or genetically interacting with the target gene, which attributes make "Regulatory gene" different from "Modifier gene" or vice-versa?
Different terms in different fields
I think that the two concepts are very similar but are used in different fields. The term "modifier genes" is often used in quantitative genetics and in evolutionary genetics while the term "regulatory gene" is often used in molecular genetics.
Example of a modifier gene that is not a regulatory gene
The concept of modifier gene can also be used in modelling when considering genes that "modify" the recombination rate (e.g. Otto and Barton, 2007; or other properties of the genome) in a quantitative manner. As such, a modifier gene is not really a regulatory gene (as it does not regulate the expression of another gene). As such I consider definitions like this one from ndsu as being too restrictive.
What I think about when I hear these terms
I would tend to think as a modifier as a more general concept than the concept of regulatory gene. Also, when I think of a regulatory gene, I think of this gene by the mechanism by which it affects other genes while when I think of a modifier gene, I think of the statistical effect of this gene on genetic properties of the organism.