Technically, the J/C/D/I/Z fare classes are used for both FC and D1 fares. So you can't tell solely by the fare class what type of fares you have. The type of fare you are booking is identified by the second to last letter of the 8 character fare basis code which will be an 'F' for FC fares and a 'D' for D1 fares. First Class marketed routes where they happen to fly D1 equipment (like ATL-LAX) have a $75 - $100 fare surcharge baked into fare (the fare surcharge is present in all domestic FC fare filings) if you happen to book an FC fare on one of the D1 aircraft (there's no surcharges for domestic coach fares on D1 equipment).

Z fares are the cheapest FC/D1 fares (mostly) and the presence of the J fare (the most expensive fare class) in one direction is what is primarily driving up the total price. Inventory availabilty on flights can change at any time and your purchase may or may not have had anything to do with it. The Z fare in one direction indicates they may have opened up inventory in a cheaper fare class in one direction. However, if you are attempting to book more seats than are currently available in a particular inventory class at once, it will force everyone on the reservation to book into a higher fare class and fare. So if your test booking on delta.com was for only one person, that might not actually be the fare you would pay for multiple passengers on one reservation.

Once the inventory in a particular class drops below 6 seats (the maximum is 9), the website will advise of how many seats are left in that fare class bucket. In the case below (booking for one passenger), there is only 1 seat left in D inventory and attempting to book more than one passenger on flight would bump everyone up to a C fare (or potentially J depending on many seats are left in C class and how many people you are booking). The "First" column below is used for both PS fares on routes that have PS fares like DTW/JFK/MSP/ATL-HNL, and FC fares on routings that don't (like SEA/LAX-HNL).