EBay is designed for national and international auctions, while eBay Classifieds is primarily designed for local sales. Potential bidders can contact sellers directly on eBay Classifieds to negotiate the price, while bidders on eBay place offers through eBay's system.
EBay typically doesn't allow sellers to place an item for sale in a particular geographical area, so people selling large items that are difficult or cumbersome to ship often use Craigslist or a similar site. EBay Classifieds is more similar to Craigslist than eBay. EBay Classifieds also allows sellers to list items for free; traditional eBay listings come with a fee that varies based on the price of the item.