First off you need to understand that a proper hanging involves a significant drop in order that the body reaches sufficient speed to snap the neck. Most suicides involve a minimal drop which results in slow strangulation of the person.
To do a proper hanging, the knot has to be somewhat substantial and arranged behind one of the ears, usually the right. The rope actually hangs slack when the victim is standing, and as well as the vertical pulling up short that occurs when the rope runs out, there's also the knot slamming against the side of the neck where the spine is located. The position of the knot is very natural for a person standing behind the victim and very difficult for a suicide to mimic.
Drop length is very important, with the drop being too short resulting in strangulation and significant time (minutes) before death to if the drop is too long the head being pulled off (effective but crude). As a murderer, you don't want to be sitting around waiting for the victim to slowly die.
An alternative form of hanging is standing the victim on the ground and running the victim up a tree. This was basically the approach used in the British Navy. Here you again want slack in the rope if you want a quick kill. The idea is to get running fast enough so that when the killer hits the end of the slack, a sudden shock is transmitted to the victim's neck, making the neck more likely to snap. If the victim is uncooperative (won't stand still) or you want the victim to suffer, you bring the victim slowly off the ground, again causing death by strangulation rather than the neck snapping. This type of hanging is virtually impossible for a suicide to mimic.
Suicides use very short drops, such as a chair. The process is gradual, taking several minutes. The knot is frequently placed in front of the ears, where it won't affect the spine, but will affect the throat (which is what you want to obstruct).
Suicides may or may not tie their hands, but even if their hands are tied, the knotting is very different from someone else tying their hands. Murderers will almost always tie the person's hands. This is needed both for the preparation stage as a person with untied hands is more of a problem to subdue enough to hang. Further, if the drop is insufficient to result in immediate death, someone with untied hands to grab the rope, pulling themselves upwards and reduce the rope's pressure. They can stay alive for a significant amount of time, until the arms become exhausted. Because of the desperation factor on the part of the victim, this means the victim could survive for half an hour or more.
The result is that a murder and a suicide look different in the details. Depending upon the expertise of the police and the medical examiner, you can tell. Most of the time relatively easily. But some can be very close calls.
Best of luck,
Jim Clark-Dawe