What’s the difference – Vigor vs Rigor

It’s been a while since I last did one of these comparison/clarification posts, but I found another example of two words that I didn’t clearly know the difference between.

I had thought vigor and rigor were basically the same thing. Upon looking them up, I had the correct understanding of rigor, but was a little off on rigor.

According to Merriam Webster:

Rigor – a (1) :  harsh inflexibility in opinion, temper, or judgment.

Examples:
They underwent the rigors of military training.
They conducted the experiments with scientific rigor.
A scholar known for their intellectual rigor

And that last one might be part of why I had them somewhat confused.

Vigor, on the other hand:

1:  possessing vigor :  full of physical or mental strength or active force
2:  done with vigor :  carried out forcefully and energetically
So, it seems they are kind of related. You can do things rigorously, and with vigor.
I clearly have a very vigorous brain to run a site like this, don’t you think?

Care to share your thoughts?