Having never been involved with either, here is how I understand it (may not be 100% correct.. but this was how it was explained to be a few years back):
Peering usually requires that a minimum amount data flow across the peer link per month. If you fall below that minimum, the peer reserves the right the charge you a penalty, or drop the peering session.
Transit usually requires a minimum to determine whether you qualify for transit or not. if you fall below the minimum, your transit connection is turned into an access connection.
Peering assumes you are using transit connections... You can get transit without peering agreements, but many times not the other way around.