In practice, anything that is within weapons range will be attacked and then followed if it moves out of range. If by following something and destroying it, a new thing comes in range to attack then that will be attacked as well. Once there is nothing in immediate weapons range, it will return to the original position. So you can see, "Local" is subjective. LRM will have a wider local range than HC or LF.

The difference between this and hold position is that anything that moves out of range will not be followed if you are set to hold position but they will attack anything in range.

From experience i would say

local is about half of the gravity well which means if u have your ships at the edge they will attack when enemy ships pass about planet marker.

Hold position your ships attacks when enemy ships come into weapon range but your ships don't move.

I think, as I wrote above, that the range is less than half of the gravity well.

On second thought. I seems that you have a point. LRF attack earlier than light frigates when set to local ranga. It is however still outside their weapons range before they are triggered.

My Initial answer was a working theory but I do know from testing that it varies by unit weapon range. I think PBhead is probably in the ballpark of weapon range + XXXX.