
Sara H. answered 04/03/19
Columbia U's Only Non-native Japanese TA, Japan Travel Coordinator
They are basically the same.
となります - change
になります - state of progressive change
This also brings up a really cool bit of information I discovered while building my lesson on ordering food in Japan for tourists:
One kind of formality which is frequently used in Japanese restaurants but doesn't make sense grammatically is ~になります. If someone brings you udon, you will likely hear them say うどんになります when they should say うどんでございます. The correct time to use ~になります is when someone at the restaurant cooks something in front of the customer or adds up the final bill!