In terms of physical movement, there really is no difference between hiking and trekking, but the activities do differ rather significantly in other ways. Both are activities in which one walks or hikes through the woods, but hiking is done more for leisure on man-made roads or trails, while trekking is done over a variety of terrain as a means of transportation, adventure, or challenge to the body and mind. Both hiking and trekking can be done over short distances in a day or two, or over a longer distance over the course of several days, weeks, or even months, but the day to day routines and activity associated with hiking will be different from that of trekking.
The biggest difference between hiking and trekking is the intensity. Hiking is generally easy to moderately paced activity, though some backpackers would argue that hiking is just as strenuous and difficult as trekking. Trekking, however, takes place over varied terrain; a trekker may travel on roads and trails for part of his journey, but he may also bushwhack through undeveloped terrain. He will often have to use maps and orienteering skills to find his way, and he must have first aid and survival skills at the ready for his trip. Hikers generally stick to established trails and do not travel over unmarked terrain.
When trekking is defined as a long-distance trip supported by porters or pack animals, the difference between hiking and trekking becomes even more vast. Trek adventures often feature people specifically hired to carry equipment, cook meals, set up tents, and so on over the course of a multi-day trip through a challenging terrain. A trekker in this case does not have to carry his or her own gear, and the activity is much less strenuous on the trekker. Compare that situation to a backpacker on a multi-day trip who has to carry his own food, clothing, safety gear, and shelter, and the difference between hiking and trekking becomes apparent.
The equipment one will need for hiking and trekking will vary according to the activity, as well as according to what type of trekking is being done. Trekkers who travel via unmarked paths will need durable equipment, and they will often need skills necessary to find or build shelter. Hikers and backpackers will need a sturdy backpack and hydration system and the physical fitness to travel the distances they have planned out beforehand.