I saw the list of books suggested by my college. There are two categories, one for text book and the other for reference book. For abstract algebra, they have Dummit and Foote, Abstract Algebra as textbook, and Herstein, Topics in Algebra as reference book. Both seem to be similar, but, don't know, the difference in how they were categorised.
In general terms, a textbook is a book you can read from the beginning to learn a new subject - perhaps on your own, perhaps in a course. Not necessarily quite that linear, since you will need to double back to reread and refresh. When you're done with the book and the course (do the exercises!) you will more or less know the material.
If you need to check some particular definition or theorem a textbook might not be the best place to look, since the idea may be spread out over several pages or sections. A reference book is likely to be more compact. (Sometimes wikipedia is a good "reference book" for things you already know something about.)
That said, both the books you ask about are textbooks, designed for an abstract algebra class. Herstein is harder/deeper/faster than Dummit and Foote. Your college is suggesting that the course will rely on D&F but that you may be able to learn a little more from a different perspective from Herstein. They may also be suggesting that you should buy D&F but consult Herstein in the library.