LE & media have been using the two park names interchangeably and/or together throughout the investigation, to much confusion.
Even from the first day of searching there, they've been sort of defaulting to calling it the
Carlton Reserve, even when they're in the
Myakkahatchee Creek Environmental Park (as you can see from
Brian Entin's Sep 18 video, where the street sign at the end clearly shows that they're on the Myakkahatchee/North Port side, where the Mustang was found)
There's a
pdf map from City of North Port here, and comparing it with the
Google Map, it does seem like BL would have started out in the Myakkahatchee Creek Park and then crossed over into Carlton Reserve via the bridge on the top part of the map, so whenever they were "on the North Port side" they were probably searching both.