No, it shouldn’t vary, certainly not by as much as you describe. Perhaps skinless and boneless in one listing and not the other?
Anyway, I can’t find anything that says one pound of chicken breast is 350 calories. The app I use says 490 for boneless skinless chicken breast. A Google search shows 499.
Raw vs cooked weight is the difference you are seeing. The back of your package is measuring raw weight while many apps/tools factor cooked weight. Search for raw weight online when trying to compare. Plus, make sure the chicken breast you are buying only has one ingredient: Chicken. Otherwise they add water and salt to up the weight and you get less meat.