"get one's head around" vs "get one's arms around"

I disagree that they are the same.

In my mind, "get one's head around" is about conceptual problems, whereas "get one's arms around" is about more physical things or actually "doing" stuff.

For example, I might say "I'm having problems getting my head around this task." meaning that I'm struggling to conceptually understand what I'm doing.

On the other hand, I might say "I'm having problems getting my arms around this task." meaning that I'm struggling to complete the actual task (but not because I don't understand).

As you can see, the distinction I draw is not a bright line in the sand, but I would say that it's consistent with how I've seen it used.

Getting/wrapping your arms around something is an old expression, something my dad used back in the '60's and my coworkers used in the '70's and '80's. It means to involve yourself in an assigned project (or job) to the extent that you are industriously engaged and providing leadership. The figurative image would be something like initially wrestling with, but eventually picking up and carrying an awkward and heavy load. Often the expression is used in the negative, to indicate that someone still needs to get their arms around something, implying that a person doesn't have a grasp on the project or job requirements and needs to get that figured out urgently.

Wrapping your head around something is a more recent term, derived from getting/wrapping your arms around something, and is more limited to only the understanding of project or job requirements. It usually does not include the additional components of taking actions to move the team towards success.