In NSDate (now Date), there's a handy property doesRelativeDateFormatting that, when enabled, returns string values such as "today" and "tomorrow" from string(from:) when appropriate in that locale:

let dateFormatter1 = DateFormatter()
dateFormatter1.dateStyle = .full
dateFormatter1.doesRelativeDateFormatting = true
print(dateFormatter1.string(from: d)) //Today

let dateFormatter2 = DateFormatter()
dateFormatter2.dateStyle = .full
print(dateFormatter2.string(from: d)) //Thurs, September 22, 2016

let dateFormatter3 = DateFormatter()
dateFormatter3.dateStyle = .full
dateFormatter3.locale = Locale(identifier: "zh_Hans_SG")
dateFormatter3.doesRelativeDateFormatting = true
print(dateFormatter3.string(from: d)) //Chinese equivalent of "Today"