What is the difference between mental and physical addiction?

Often together. The 2 of these often come together. "addiction" signifies a behavioral pattern of using a substance despite obvious harm to the person's life, work, and relationships. They use more than intended; lie about using; and spend lots of time using it. Physical habituation (having withdrawal symptoms when missing dose) can happen without addiction, but may come with mental/behavioral patterns as above.
Addiction. Physical tolerance to a substance can mean that more & more of it is needed for the same effect; physical addiction can mean having withdrawal symptoms from that substance when without it. "mental" addiction involves the behaviors one does with the substance. People often use more than intended; cannot stop once they start; lie about use; pursue the substance despite bad effects on rest of life.
No difference. In my opinion. Mental or psychologic addiction is still due to physiological changes although limited to that part of the brain that controls our emotions. Appetites, motivation and learning. Its all physical.
Physical addiction. Is continued use to avoid unpleasant physical symptoms when not using.
Behavior. Many drugs can cause physiologic dependence, as the body adjusts to them. Abrupt discontinuation may evoke an uncomfortable withdrawal syndrome. This is different from the psychological disorder of addiction, in which there is preoccupation with and loss of control over use of a substance which causes distress and major changes in interpersonal function.