I think that technically speaking self-striping yarn is a self-patterning yarn inasmuch as stripes are a pattern. Self-patterning yarn generally refers to yarn that makes a more complex pattern, or at least I think so. What Is Self Patterning Yarn? I'm glad you asked,
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Huh. Most of the stripes I've done I've used multiple colors, but here's one from Knitpicks Parade. It has a bit of pattern on the gray stripe, but not all self striping do. The socks were sort of self patterning, but that means there is patterning on the stripes.
Keep in mind that with all these types of yarns the width of the project affects stripe width.
When asking questions ALWAYS post the name and a link for the pattern if you have it.