It's possible to receive a call and a message notification simultaneously, thus seeing two notification banners. This could occur if you are available on both Voice and Messaging and because Voice operates on an independent routing queue, separate from other Channels.
If you accept the call, you won't receive any requests from other Channels while the call is active.
If you accept the messaging request (e.g., chat), your Messaging Channel concurrency settings determine how many Customers you can work with.