The differences between nurseries and garden centers within big box type home improvement centers should be more obvious. Contrary to all the fancy marketing, a big box garden center really is just another of many departments within a larger home improvement center. A good nursery specializes in plants, and only plants. A sales representative in a big box store might have been selling paint or refrigerators last week. A nurseryman in a real nursery works regularly and more exclusively with horticulture.
It is probably safe and most likely significantly less expensive to obtain common and resilient plants from big box garden centers. Crape myrtles (ick!), oleanders, pittosporums, junipers and photinias seem to be healthy regardless of their respective origins. However, more unusual varieties of more unusual plants, or plants that are likely to be damaged by a bit of neglect, are either unavailable or likely to be of inferior quality in big box garden centers. Only the most common and resilient cultivars (varieties) of rhododendrons, flowering cherries, flowering dogwoods and fuchsias are marketed. If they get damaged, the damage may not be noticed by the possibly undiscriminating staff.
Nurseries are not only able to maintain their stock better, but can maintain a much more extensive selection of different types of plants. The more finicky types of ferns, columbines, azaleas and Japanese maples are no problem. Experienced horticulturists are familiar with the plants that they work with, and can make recommendations for those who might need help with selection. The prices are often more expensive, but are justifiable to those wanting specific plants that can not be found elsewhere.
A few wholesale nurseries that procure nursery stock for the landscape industry are open to the public for retail. Their retail (not wholesale) prices can be comparable to those of big box garden centers. The selection is different, which means that they lack many plants, but have a few others that the big box garden centers lack. They have plenty of horticultural expertise, but not much sales staff.