Update `print` doc (#18053)

src/lightning/fabric/fabric.py

@@ -476,7 +476,8 @@ class Fabric:
         return move_data_to_device(obj, device=self.device)
 
     def print(self, *args: Any, **kwargs: Any) -> None:
-        """Print something only on the first process.
+        """Print something only on the first process. If running on multiple machines, it will print from the first
+        process in each machine.
 
         Arguments passed to this method are forwarded to the Python built-in :func:`print` function.
         """

src/lightning/pytorch/trainer/trainer.py

@@ -1069,9 +1069,8 @@ class Trainer:
         self.profiler.setup(stage=self.state.fn, local_rank=local_rank, log_dir=self.log_dir)
 
     def print(self, *args: Any, **kwargs: Any) -> None:
-        """Print the arguments to standard output. When running on multiple devices on a single node, this method
-        will only print from one process to avoid redundant outputs. When running across multiple nodes, this
-        method will print from one process in each node.
+        """Print something only on the first process. If running on multiple machines, it will print from the first
+        process in each machine.
 
         Arguments passed to this method are forwarded to the Python built-in :func:`print` function.
         """