Do the two phrases mean what i proposed below?

Let's go grab some lunch

Meaning: go and have a quick lunch, maybe sandwiches or something similar.

Let's go pick up some lunch

Meaning: go and pick up some take-away and have it at our home or office or whatever.

Do the two phrases mean what I proposed below?

Let's go grab some lunch

Meaning: go and have a quick lunch, maybe sandwiches or something similar.

Let's go pick up some lunch

Meaning: go and pick up some take-away and have it at our home or office or whatever.