How come some people snore, while others make noise with their teeth when they are sleeping?

We're all different. The two are not necessarily related. The causes of snoring can be sinus congestion from cold/allergies, enlarged tonsils or even by the soft posterior "skin" of the upper palate losing elasticity. These may or may not be accompanied by apnea (periods of not breathing). Making noise with the teeth is caused by clenching or grinding (bruxism). This can be stress related and/or TMJ related.
Different Things. Snoring is an obstruction of the airway, usually due to the tissues at the back of mouth & the base of the tongue falling backwards. Bruxism is grinding of teeth which can be from tension or malocclusion of the teeth. There are dentists who have training and experience treating both bruxism and snoring, often as part of a cooperative treatment plan with physicians.