Stylish, fashionable, modish, smart, chic, dashing can mean conforming to the choice and usage of those who set the vogue (as persons of wealth and taste or often the avant-garde).
Stylish is likely to stress currency and, correspondingly, transitoriness.
Fashionable is often interchangeable with stylish , but fashionable is distinctly more likely to imply conformance to what is established and generally accepted than to a transitory or restricted vogue.
Modish stresses conformity to the latest styles, but sometimes it suggests a step beyond what is describable as stylish or fashionable and may apply to what from another point of view might be called daring , extreme , or startling .
Smart comes close to modish in suggesting the height of what is stylish or fashionable, but it implies a position in the forefront of what is acceptably stylish or fashionable rather than one beyond this point.
Chic is sometimes used simply as an equivalent to modish or smart or even of fashionable . However it may not imply conformity to the latest style so much as an effectiveness in style which suggests the exercise of a knack or skill and the achievement of distinction.
Dashing applies to people or to things which they wear or use; it implies not only stylishness or, more often, modishness but a bold, shining quality that enables one to cut a figure in any group or assemblage.