Do I understand this correctly?
I'm trying to understand the difference between "Go on vacation" and "Go on a vacation."

What I understand from my research is:

"To go on vacation" means to take time off from work/school, but it doesn't necessarily mean that you travel to a new place, you can just rest at home, for instance.

Whereas "To go on a vacation" always implies that you travel to a new place.

But in the end, “on vacation” and “on a vacation” are used interchangeably in American English.
Do I understand this correctly?

Question

Do I understand this correctly?
I'm trying to understand the difference between "Go on vacation" and "Go on a vacation."

What I understand from my research is:

"To go on vacation" means to take time off from work/school, but it doesn't necessarily mean that you travel to a new place, you can just rest at home, for instance.

Whereas "To go on a vacation" always implies that you travel to a new place.

But in the end, “on vacation” and “on a vacation” are used interchangeably in American English.
Do I understand this correctly?

Answer

I’m on vacation.  (Not working, possibly traveling, possibly not)
I’m on a vacation. (Not working, traveling)
I took vacation. (I took time off from work)
I took a vacation. (Usually travel)
I went on vacation (Travel)
I went on a vacation. (Travel, maybe adding “a” suggests a bigger trip)
I went on vacation to the mountains.
I went on a vacation to New Zealand.

Answer

They are not used interchangeably in American english. On vacation means you are not working while on a vacation usually means travel was involved. "On vacation" is like saying you are on holiday while on a vacation is like saying you are spending holiday somewhere.

Answer

To go - means to leave somewhere 
Vacation means -a period of time spent away from your day to day activities like work, school, home life, So you just to Go and relax.

Answer

This is a reasonable way of saying it, yes. "Going on vacation" or "taking vacation" means taking time off from work and may or may not include destination travel. "Going on a vacation" or "taking a vacation" typically implies a change of scene, a trip of some sort.