The "active" designation for the second partition on your hard drive...indicates that there is a Windows partition there.
Ditto for the Acer partition.<<Some of these programs work...>>
Any programs installed on the Windows partition reflected on your current external hard drive...can only run under certain circumstances.
a. You reinstalled said program on the Acer partition on the newer hard drive
b. You set up a dual-boot...with both hard drives containing bootable XP installs
You cannot run any program installed on the current external drive...by any other method I know, it just cannot happen.
If you are saying that you can...I'd have to say that you are mistaken.
As for access...you can access any file on either drive, that's normal. Running programs installed on an external hard drive which are not installed on internal hard drive...cannot happen...unless you boot into the version of Windows on that external drive.
This is pretty basic.
If you had cloned your old drive to the new drive...the same programs would have been installed on each.