Are the types essentially different sets of traits?

From People Types and Tiger Stripes, written by Gordon Lawrence and published by CAPT.

No. Type and trait represent different ways of looking at our psychological natures. The types can be identified by their differences in traits, and they are described by their traits. For example, in the table "Brief Descriptions of the Sixteen Types," the descriptive words and phrases used for each type represent traits. But the type preference categories are not traits. Rather, they are mind-sets, distinct ways of processing experiences that become visible as traits. For example, extraversion as a type preference is an either-or category, not a trait that is measured as more or less, or degrees of skillfulness. Because this question is too complex for a good short answer, a portion of Chapter 2 covers it more fully.