Those terms are an American invention. As for Italy

• Latte = plain old milk. Can be cold or hot, it’s milk
• Caffelatte = probably the origin of the American “latte”, literally means coffee and milk, usually made and home with cold or hot milk and moka coffee
• Latte macchiato = big cup of milk, frothy on top, with a shot of espresso in it
• Caffè macchiato = espresso with a shot of milk, can be frothy