Cut back vs cut down

These words seems similar. Can you give me more explanation about them?

These are the free dictionary differences of cut back vs. cut down.

cut back

  1. To shorten by cutting; prune.
  2. To reduce or decrease: cut back production.

cut down

  1. To kill or strike down.
  2. To alter by removing extra or additional fittings: cut down a car for racing.
  3. To reduce the amount taken or used: cutting down on one’s intake of rich foods.

Here is the link: Cut back - definition of cut back by The Free Dictionary as there are other examples with phrases using the word “cut”.