Contacts are existing relationships. Frequently, Contacts will be associated to a business opportunity or Deal.
Leads are unqualified business relationship or sales prospect you have yet to converted into Deals. Leads will exist exclusively in your leads tab until such time they become associated to a Deal. Once you convert a lead into a Deal, the lead will be removed from the worklist, and you can manage the relationship from the Deals tab. This simultaneously creates a contact record in PipelineDeals. Contacts are considered existing relationships that you've added into the Contact tabs or people associated to deals.
Contacts could also include vendors, perspective investors and other relationships you want to keep track of.