To many people, Dijon-style mustard is regular mustard. Another group of people think that the common yellow mustard you refer to is called "prepared" mustard, but any fluid mix of crushed or ground mustard seeds with seasonings and vinegar, wine, water, beer, or must (fresh-pressed grape juice) is a prepared mustard (in Britain, a "made" mustard). What you are referring to as regular mustard is best called yellow mustard or perhaps American-style mustard.
There are, of course, many types of prepared mustard with many flavor variations. There are three main types in France. Dijon is light in color, but fairly strong in flavor. Bordeaux is darker, with a milder, but more vinegary flavor, and includes sugar and usually tarragon. Meaux mustard is made from crushed mustard seeds rather than seeds ground to powder, and is generally mild.
German mustards, of which there are many, are generally of the Bordeaux type. English mustards are the strongest overall and can be a shock to the uninitiated. American yellow mustard is a mixture of the mildest mustard seeds with vinegar, sugar, and turmeric, which makes it yellow.
There is such a flavor difference between yellow mustard and Dijon mustard that we do not substitute one for the other in general. Why not buy a small bottle of Dijon-style mustard and give it a try? Even if it tastes very unusual at first, you may really appreciate what it does in this recipe - and others.