What is the difference? Doing tai-chi form in the correct way will result in a feeling of sluggishness, like there is some internal resistance that one has to overcome. And THAT is the proper exercise element of tai-chi. In contrast, simple morning exercise has little internal resistance.
What is the resistance causing the sluggish feeling (and such resistance required energy to overcome)? Firstly the resistance comes from the condition of muscle-as-one (肌肉如一). When one moves, one has to carry the total muscles along! And THAT causes the sluggish feeling. And to achieve muscles-as-one, the practice of zhan zhuang is essential. Secondly, the resistance comes from joint-opening. When one tries to open a blocked joints (by definition, all joints can be further opened, and therefore for the purpose of tai-chi, we should consider all joints as blocked). In order that blocked points can be targeted, one needs to be mindfully focused (in chi-kung terminology it is called point meditation).
Where does the energy in overcoming the resistance comes from? In comes from two areas (in addition to the breathing muscles, which can best be tackled in meditation, so I shall leave this area to other posts). Firstly it comes from gravity. When our body is totally relaxed, the force of gravity can exert maximum force upon our body (people having experience in handling old people can understand what I mean - those totally relaxed old folks are truly HEAVY!). Secondly it comes from inertia (once in motion, a body will continue to move assuming no opposing force). Again here, a relaxed body can create the most powerful inertia when we move (or to use a better word/concept: flow, or fluidity of movement) our body SLOWLY, resulting in less opposing force.
Observant readers can perhaps conclude the following requirements of tai-chi:
1. Practice zhan zhuang to create the condition of muscles-as-one
2. Do meditation to learn how to do point focus or point meditation.
3. Focus your mind, always
4. Do it slowly and fluidly
5. Totally relax your body
If you aren't practicing along the above path, perhaps you are not practicing tai-chi at all!