Under, below, underneath son sinónimos.

El hombre está debajo del árbol.
= The guy lies under the tree.
Ejemplo
The cat is under the table.
The cat is underneath the table.
El gato está bajo la mesa.
You find my letter under your grammar book.
You find my letter underneath your grammar book.
Encontrarás mi carta debajo del libro de gramática.
There is lots of dust under his bed.
There is lots of dust underneath his bed.
Hay mucho polvo debajo de la cama.