According to some, there is technically no difference in Modern English between the terms gourmet and gourmand. Both have the meaning typically ascribed to gourmet, a person who enjoys and appreciates fine food. However, the two terms differ in their connotative meanings.
Many English speakers feel that gourmand implies a tendency towards gluttony and that a gourmet is a somewhat more reserved individual. The first may be more of a hedonist and the second considered more of a critic, though both are connoisseurs. In older or more conservative usage, gourmand is closer in meaning to glutton.
Both words are borrowings into English from French. In French, gourmand originally referred to a glutton, but the word evolved to mean a person who enjoys fine food in Modern French. Therefore, the English term is closer in meaning to the older French definition, which existed at the time the term was first incorporated into English. Recently, the English word has begun to evolve the same way it did in French.
Gourmet, on the other hand, is a corruption of the old French groumet, meaning "servant" or "wine steward" and also a cognate with the English groom. Its modern meaning in both French and English, as a person with refined culinary tastes, was influenced by the word gourmand. While some who self identify as gourmets may object to being called a gourmand, the distinction between the two is certainly not set in stone, and the use of either term could be justified.
One important difference between the terms is that gourmet may be used as an adjective as well as a noun. Fine foods and wines and nearly anything involved in their production or preparation may be referred to as gourmet. Therefore, it is common to hear of gourmet chefs, restaurants, and cookbooks, to name a few.