A startup casual dress code generally entails a nice pair of jeans (think dark-wash, rather than ripped or light-wash) or a pair of casual khakis, with a top that is professional (such as casual button downs, a light sweater and in some cases, a nice t-shirt) but more relaxed than tradition business wear.
Startup casual outfits generally have a more modern vibe than business casual clothing. At the same time, because working at a startup can involve long days and impromptu or unforeseen tasks, the clothing should be comfortable and wearable.
If you're interviewing at a startup, you probably wouldn't want to show up in head-to-toe business attire. Leave the black suit and dress shoes at home, but keep in mind that for an interview it's imperative you look polished and professional, no matter how casual the company might be.