Ernest, this is a great question because learning styles and multiple intelligences are often perceived as similar models or even part of the same model. There are some similarities and many differences.
A difference between the two models is found in their names—Multiple Intelligences and Learning Styles. The fundamental construct of Gardner’s theory is intelligence, whereas the Dunns’ is learning. There is a world of difference between the study of intelligence and learning and, of course, the two constructs share broad territory also. Gardner’s theory about multiple intelligences “makes no claims whatsoever to deal with issues beyond the intellect” and it was “a theory that was developed without specific educational goals in mind” (Gardner, 1995, p. 103). In contrast the Dunn and Dunn Learning-Styles Model’s purpose is to improve academic achievement by matching how a person learns, her/his learning style preferences, with the ways s/he is taught.
Gardner defines intelligence as “a biological and psychological potential; that potential is capable of being realized to a greater or lesser extent as a consequence of the experiential, cultural, and motivational factors that affect a person” (Gardner, 1995, p. 102).
The Dunns define learning style as “the way in which each person begins to concentrate on, process, internalize, and remember new and difficult academic content” (Dunn, Denig, & Lovelace, 2001, p. 12).
The similarities between the two theories are primarily linguistic for example both use the term kinesthetic, Gardner refers to kinesthetic intelligence, which we witness when watching a ballet. The Dunns found some learners needed to be physically engaged with their whole bodies to learn new material, whether it is Algebra or the tango.
That is a very short answer for a complex question and I hope it provides some illumination on the subject. I am happy to discuss it further. Below are the articles I cited, plus a review of multiple intelligences by Gardner.
Reflections on Multiple Intelligences, H. Gardner (1995).http://www.psych.udel.edu/~kuhlman/cakee/AEP98.5.22.PDF
Two Sides of the Same Coin or Different Strokes for Different Folks? Dunn, Denig, and Lovelace (2001). Teacher Librarian, 28:3.
Multiple Intelligences After 20 Years, H. Gardner (2003).http://www.pz.harvard.edu/PIs/HG_MI_after_20_years.pdf