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Peering is when you send packets from your network (or your customers' networks) to my network (or my customers' networks). Transit is when you send packets from your network (or your customers' networks) to my network, and I agree to deliver it, regardless of if it's within my network, my customer's networks or beyond my network (via peering or my own transit connections).

Peering is historically settlement free at public exchanges and in private connections with balanced traffic. When a private peering is not balanced, historically the peering would be disconnected, but in the mid 2000's, paid peering started showing up more frequently as an option. Paid peering is often less expensive than transit, but it depends on the networks involved and the volume.