Black-capped Chickadees have whiter edges on the wing feathers and brighter, more-buffy flanks. Carolina Chickadees are subtly drabber with less white on the wings. Differences are most pronounced with fresh plumage.
Black-capped Chickadees have a white nape and Carolina Chickadees have a subtly more gray nape, but I don’t find this field mark particularly useful unless you have the birds in hand or really good photos.
Identification in the overlap zone is often possible, but some intermediate individuals are best left at the genus level as hybrids occur and the differences between the two species become less distinct as the plumage ages/becomes worn (i.e., differences are most distinct in fall and winter after their annual molt).