They are not the same thing

Thyme is an herb of culinary and medicinal value that is selected from species of the genus Thymus, and is rich in iron, while its aroma and antiseptic properties are derived from its own thymol. It reaches a maximum height of about 40 centimeters and grows in Europe, North Africa and Asia. It is generally an evergreen plant with a narrow, thin stem. It has medicinal value and can be used to repel mosquitoes, is pungent and slightly warm. Expels wind and relieves pain, relieves cough and lowers blood pressure. Used for cold, cough, headache, toothache, indigestion, acute gastroenteritis, hypertension.

Thousand Mile is a small tree plant in the family of Rutaceae. Born in low hills or high altitude mountains in open or dense forests. Limestone areas are more common, granite areas are also found, sometimes for a small area within the single superior species. The roots and leaves are used as herbal medicine. The flavor is slightly pungent, bitter and spicy. It is warm in nature, slightly poisonous, opening the meridians, moving qi, activating blood circulation, dispersing blood stasis, relieving pain, suppressing fright, subduing swelling, and detoxifying. It is used for treating cold, headache, stomachache, toothache, rheumatism, bone pain, bruises and swelling.