Example 1
Can we go inside? It's so cold out here that I can see my breath.
That's condensation for you. When you exhale in Minnesota in January, the water vapor in your breath turns into tiny drops of water that you can see. As you can also see, breath is the right word here because we're talking about air expelled from the lungs. Now go inside and get some hot chocolate with extra marshmallows.
Example 2
The panicked baker was told to breathe deeply after his life-sized Andre The Giant cake collapsed and pinned his legs.
That's a lot of frosting. In this sentence, breathe is the right word because we're talking about a scared, trapped cake-maker trying to take deep breaths.
Example 3
Before legendary comedian Groucho Marx took his last breath, he uttered one final wisecrack: "This is no way to live!"
In this sentence, breath is the correct word because it refers to a gasp of air in the lungs. And as anyone who has ever seen A Night at the Opera or any other Marx Brothers film would attest, it's totally unsurprising that Groucho would go out on a joke.