When I save a phone number to a contact from a received phone call, iOS includes the US country calling code "1" at the front of the number (eg
1 (999) 555-1234).
When I save a number from a received text message, iOS or macOS adds the US country code "+1" to the front of the number (eg
+1 (999) 555-1234).
The discrepancy by app (Messages vs Phone) in formats of saved numbers might differ per carrier (mine is T-Mobile—does your carrier handle differently?). It's certainly messy to see numbers auto-saved differently, which is annoying. Also noteworthy: iOS adds neither a one nor a plus-one to five-digit robo-numbers that I save.
Everything works fine with "+1" or "1" or nothing before the area code, when using my SIM-free phone for US numbers while within the United States.
But when I manually enter new phone numbers into Contacts app on iPhone or MacBook, should I best save them with "+1" or "1" or with nothing before the area code? Which format is more future-proof (such as when local or national calling rules change)? Which is better for international travel?