A start is a quick reactive reflex or jerk (type of quick motion) that ends immediately. It may last one second or less. A shiver is a longer sensation that causes your body to shake (or "vibrate") from fear or cold. It may last anywhere from several seconds to a minute or two.

To "start" can mean what you do when you are "startled." It means one, single, involuntary muscular reaction. When I am dozing in my easy chair, I startle easily. For me it's a whole-body reaction--I leap partway out of the chair, I wave my arms a bit, and I make a noise like "Wauggggh!" When it is over, it is over. It's one single big, jerky muscular reaction. To "shiver" is a continuous, extended shaking, trembling, quivering, or vibration. It goes on for a while. The most common reason is that you are cold. Shivering is an involuntary reaction to cold. It makes the muscles work, produce heat, and create physical warmth.

"To start" is the same as "to begin". Shivering is when you shake because you're cold or scared.