Path is more common for these examples:
He had to walk along a path across the lawn.
I stand in homebody's path.
The atoms cross the physical paths.
Way is used in these examples:
I take the way back. => it's a general way, not especially with a visual mark from A to B.
He takes this way. => to give the direction
It will be a long way from here. => distance
In this way I won't agree your decision. => manners
They are friends from way back. => old relationship between two friends
He had to walk along a path across the lawn.
I stand in homebody's path.
The atoms cross the physical paths.
Way is used in these examples:
I take the way back. => it's a general way, not especially with a visual mark from A to B.
He takes this way. => to give the direction
It will be a long way from here. => distance
In this way I won't agree your decision. => manners
They are friends from way back. => old relationship between two friends