As stated, the manuals have more info about how various functions work, more so than what I can explain in a post, there is a section in the settings to accommodate DND -
However, the statement in the last screen shot about the call dropping is only when there is no voicemail configured for the extension.
The key to it is understanding that presence is about the extension owner. DND is about the status of the extension. You will see this when you do the pull down box as I showed in the first screen shot. As you go thru the status offerings the tab will move in conjunction with the selection with the exception of DND.
The point being that when DND is set, it means that you do not want the phone extension to be bothered, so if a call were to come in, it goes to the VM, assuming same is configured. So, logically, you never wanted DND in the first place, you simply wanted any call destined for that extension to be sent elsewhere; hence call forward unconditional-
DND is simply a way of taking the phone out of service, but still retaining the calls within VM so the extension owner can deal with them later.
Now then, you will also note that the UCM has the ability that when the phone is in DND, you have the ability to make exceptions such that you can allow certain numbers through, but unless the UCM is managing the DND aspect (remember that I indicated that both the phone and UCM have certain common functionalities) the function will not work.
As stated, the phone also has some of the same features built-in. This is because the phone may mot be connected to a PBX, but perhaps directly to a provider or to a less featured PBX that may not have some of the desired functions. When you set DND at the phone, calls are still sent to the phone and the phone will reply with a 486 Busy response. When you set Busy at the UCM, as Marcin has suggested by synchronizing the function, the UCM will know the extension is busy and never send the call to the phone but will instead immediately follow the rules set for that presence status and condition. When you have call features enabled in the phone, the phone will take over the features so should you use the dial code to forward, the forward will be in the phone, not the UCM.
Each phone system make will likely have some nuance or twist as to how they may accomplish what seemingly is the same function, but one has to read the manuals to get a feel for how things work and then experiment as many manuals (to include GS) are often lacking the clarity that many need/want.
Me, I do not enable the call features on the phones when connected to a UCM, I want the UCM to control things as I find that users will play with the phone settings and inadvertently set some function that I would otherwise have to go and hunt down and reverse.