Even i had confusion differentiating between these two terms at the beginning ,
have a look at this explanation from one of the Award winning DSP books.

![enter image description here][1]


Amplitudes,

![enter image description here][2]

Magnitudes,

![enter image description here][3]

![enter image description here][4]


  [1]: https://i.sstatic.net/hLziY.png
  [2]: https://i.sstatic.net/P47CO.png
  [3]: https://i.sstatic.net/7Sg2R.png
  [4]: https://i.sstatic.net/EhLYs.png