"Dream of" vs. "dream about"

What is the difference between the usage of dream of and dream about? For example,

I dream of becoming a doctor.
I dream about becoming a doctor.

I dream of going to places.
I dream about going to places.

If I mean dream as in dreaming while I am asleep, then which is preferable?

'I dream of' is usually talking about your goals/aspirations. So

I dream of becoming a doctor

means

I want to become a doctor some day

and 'I dream about' usually talks about your actual dreams. So

I dream about becoming a doctor

means

I have actual dreams in which I become a doctor.

'I dream of' is usually followed by a verb:

I dream of winning the World Cup

'I dream about' is usually used when referring to a noun:

I dream about chocolate ice cream

However, I have seen these used interchangeably.