Noise differences - The Freeagent probably has the heads rest in the landing zone when not in use. The other one probably doesn't, and you're hearing the sudden attempt to move the head. It could also just be the difference in the drive motor for the platter.
Yes - With USB "hard disks", there is a spinning platter that holds the data. On both sides of that, a head that reads and writes the data is within 1mm (actually much less) of the spinning platter. When it has power, the head moves back and forth when getting / writing data to the disk. The head then goes back into a safe position, off of the surface of the platter (or at least on a "landing zone" on it.
If the read/write heads land on the spinning or stationary platter instead of the landing area, say goodbye to your data (at least some of it).
The noises you are hearing is probably the electronics trying to send one last "return home" message to the head controller, and the head trying to move. When you pull the power on the drive, there may not be enough time and power to move the head all the way into the landing area. They are designed to try to go there automatically, but it's the reason (among others) that you aren't supposed to pull the power on a computer.
When you shut down a USB HDD or computer, the controller (for the computer's internal HDDs) or the USB controller (on the USB HDD) tells the drive to make itself safe. It can do that quite quickly, then won't allow the head to move again until it's initialized. When you pull power on any spinning disk drive, you are taking away all ability to control the head. You're left with physics (air moving along with the disk presses against the head, pushing it into it's landing area) - The problem is that if conditions aren't pretty near right, it won't put it entirely in the landing area and it may scratch your disk (and destroy the read/write heads), causing data loss.
That being said, USB Flash drives are much different, but still should be removed "safely". Windows (and other OSes) will look like it finished moving that 10gb movie over to your flash drive, but it's really finishing the last 10% or so in the background. While it's doing that, if you unplug the drive, it will mean the file is not recoverable. If you happen to do that when the OS is writing the file table, the file table becomes corrupt and must be repaired, and data loss may occur. This same process occurs with both hard drives and flash drives, internal and external.
So, yes, ejecting a drive "safely" is important, especially with spinning disks. Windows Vista and higher reduces VSS(Volume Shadow Service) interaction with the drives automatically, reducing that risk, but unless you haven't used the drive in quite some time, it's not generally safe (just in-case).
For more information, see Volume Shadow Copy, Hard drive failure, about "Head Crash" - Also has good info about landing zones and the rotational force being used to propel the head into it's safe landing zone.