No. Clean, non-sterile gloves are the standard for home dressing changes, and the advice is the same across different kinds of wounds.
When caring for a closed surgical wound, put on clean medical gloves if your wound is infected (red or oozing) or if you are changing the dressing for someone else. The gloves do not need to be sterile.
When caring for an open surgical wound, use a clean (not sterile) medical glove to grab the old dressing and pull it off.
For wet-to-dry dressing changes, put on a pair of non-sterile gloves. Then change them twice more during the procedure: a new pair for cleaning the wound, and another new pair for applying the new dressing.
That last point is the one worth taking away. What matters less is the gloves being sterile, and what matters more is changing them between stages, with handwashing in between. Removing an old dressing, cleaning a wound and applying new packing are three stages, and the same gloves do not carry across them.
Gloves aren’t needed every time, either. For a closed surgical wound, they’re called for in two situations: an infected wound, or a dressing being changed for someone else. They aren’t required for every dressing change on your own wound. What you do need every time is clean hands.
If you have been given different instructions, including sterile technique for a particular wound or device, those were given for a reason and come first.