NFL Connections #42, Answers
The full solution: all four groups and the 16 names, sorted from the easiest group to the trickiest.
Most career passing TDs
Tom Brady, Drew Brees, Peyton Manning, Brett Favre
Most career rushing TDs
Emmitt Smith, LaDainian Tomlinson, Marcus Allen, Adrian Peterson
Most career receiving TDs
Jerry Rice, Randy Moss, Terrell Owens, Cris Carter
Most career receptions
Larry Fitzgerald, Tony Gonzalez, Jason Witten, Marvin Harrison