All commercial cotton preparations are called sliver—cotton is never called “top”.
Card sliver is the result of the first process, carding. The fibers are not all parallel, and because of this, there is more loft to the preparation (more air space). Beginning spinners do well to start with card sliver, and most spinners will choose it as the easiest to spin.
The next process is drawing, where 8 to 10 ends of card sliver are run side by side through rollers and drafted out to be about the same size as one of the input ends. The result is called a “draw blend”. I use this technique to obtain striped sliver. The fibers are mostly parallel and there is less loft in the preparation.
For high quality yarns, combing is performed. Combing removes the short fibers, making the fiber length more uniform. There is little air space and the preparation is very dense. There may be up to 15% waste removed in combing, so the sliver and yarn are more expensive. Uniform fiber length means that properly spun yarn is unlikely to pill or abrade easily.