In A Designation Story (http://thanlont.blogspot.com/2011/10/designation-story.html), I discussed why the WF-2 was a -2 and not a -1.
In it, I mentioned the TF-1, which was the Carrier On-board Delivery (COD) derivative of the ASW S2F as the WF-2 was the AEW derivative of the S2F. I also wrote about the TF-1 in my summary history of COD, http://thanlont.blogspot.com/2011/05/carrier-onboard-delivery.html
All these years, it had never occurred to me that the T in TF didn't make sense for a COD. At the time, T was the mission designation for trainer. The Navy mission designation for transport was R (I don't know why) or JR, if it was a utility transport (I don't know what the difference is between a utility transport and a regular transport is either). So strictly speaking, as a transport it should have been designated RF or a JR3F (there was a JRF and a JR2F). In the 1962 DoD-driven redesignation of Navy airplanes, it was rightfully given a C for Cargo designation, C-1.
It turns out that for some reason, the Navy decided that it would be designated a trainer. And of the five missions listed on the TF-1 SAC, three are training, including the first two: