Loudness
Tap a drum gently, then hit it hard. The first sound is soft, the second loud. The difference is loudness.
Loudness
Loudness is the sensation the ear feels that depends on the energy carried by the sound wave.
Loudness and amplitude
Pluck a stretched string. The further it is pulled from its rest position, the louder the note. Pulling it further takes more work, so the string gives more energy to the sound wave. A string pulled further has a larger displacement — it vibrates with a larger amplitude, and so does the sound wave it produces.
A larger amplitude of vibration gives a louder sound; a smaller amplitude, a softer one.
Figure to be added