What is the difference between Fix and Repair?

Fix: 

1- We use it to restore something as a whole and get it back to how it was before. 

2- It is more common to use in everyday speech.

Example:

My dad tried to fix the door yesterday.

Repair:

1- We use it to restore a part of something by someone with expertise.

2- It is more formal.

Example:

The mechanist repaired my car since the engine broke.

Note: We can say a repair shop or a repairman, but we can not use 'Fix' instead.