No, both the Drag Hesitation and the Change of Direction begin forward on man's LF, turning to the left. The difference is what happens after the feet brush on step 3: In a Change of Direction, the man steps LF forward, whereas in the Drag Hesitation, he steps back on his LF with lady outside partner.
In the ISTD manual, the Drag Hesitation is listed at the very end of the book as an "approved variation" in silver Waltz. As for the Change of Direction, that's mainly considered a bronze Foxtrot figure, but oddly enough is also found in the final pages of the ISTD manual as a bronze/Associate Quickstep approved variation.
One notable difference between the Foxtrot and Quickstep versions of the Change of Direction is that the final step on man's LF is treated differently: In Foxtrot, it is its own step, which is to say that the following pattern should be one that begins with the man's RF forward, such as the Feather Step. In Quickstep, however, it's treated as what I call an "overlap", which is really the first step of the following pattern. Hence the Change of Direction in Quickstep is followed directly by a left-turning figure beginning with man's LF, such as Chasse Reverse Turn or Progressive Chasse to R.
Papicolle: The mislabeling sounds like a simple mistake which should be easy enough to correct. Thanks for the tip!
Regards,
Jonathan