Is there a difference between a doctor going with a request to terminate treatment that result in a patient death and a doctor intentionally giving a deadly drug?
Or withdrawing artficial nutrition or hydration
There is a great difference between these.
Unless a doctor is in a jurisdiction in which physician-assisted suicide is legal, the doctor is committing murder by giving a deadly drug. There are no gray areas here at all from a legal perspective. There might be some gray areas from an ethical perspective, but a doctor who does this can certainly be prosecuted and could very well be found guilty.
A patient's request to terminate treatment is a different matter altogether. While the doctor is providing a means of death by not treating, the doctor must respect the patient's wishes because a patient is within his or her rights to decline treatment, and the doctor is not doing something "active" to kill the patient. We make a distinction between doing something, which is active, and ceasing to do something, which is considered more passive.
I should point out that in the law, there are situations in which once one undertakes a duty to someone, that duty must be followed through on. For example, if you save someone from drowning and then leave him on the beach below the tideline, you might be liable for his death. But this is not the case in this situation because the patient has the final word on treatment or lack thereof.