Wikipedia offers a nice overview. Here are the important quotes:
The Sanskrit word yoga has many meanings, and is derived from the Sanskrit root "yuj," meaning "to control," "to yoke" or "to unite." Translations include "joining," "uniting," "union," "conjunction," and "means." The word yoga may also derive from the root "yujir samadhau," which means "contemplation" or "absorption."
[Patanjali gives this terse definition] "Yoga is the inhibition (nirodha?) of the modifications (vrtti) of the mind (citta)".
Hatha Yoga is a particular system of Yoga described by Yogi Swatmarama compiler of the Hatha Yoga Pradipika in 15th century India. Hatha Yoga differs substantially from the Raja Yoga of Patanjali in that it focuses on shatkarma," the purification of the physical body as leading to the purification of the mind ("ha"), and "prana," or vital energy.
If this is accurate, there is a strong possibility that Yoga and the Daoyin--Tai Chi--Shaolin matrix have a common origin, or that at least they all stem from a common notion of what a human being is. I would summarize the method of Daoyin as--- "yoking" a purified physical body to "that stuff which animates us" (qi or prana) and then "yoking" that to a larger active spacial mind. ---The use of the word purification here could also mean distillation or total differentiation.
The jing and qi must be purified or distinguished, they can not be mixed. If the physical body (jing) is mixed with prana/qi the result will be gross motor or fine motor movement. All three types of movement are controlled by the spacial mind, however in the case of "yoking" or Daoyin the spacial mind does not effect the body directly it must first unify with the qi/prana which then acts as an intermediary pulling (or pushing) the whole physical body along. So fine motor movement, like typing, is almost impossible to do because it requires direct mental control of the fingers.
Pantanjali's "inhibition of the modifications of the mind," may simply be describing the discarding of all fine and gross motor control. Perhaps it also includes the discarding of artifice, effort, and the maintenance of fantasies. That would put it pretty close to an early definition of Laozi's key concept: wuwei (not doing, or non-aggressive intentionality).
A quick scan of blogs dealing with the question of "yoking" turned up this:
Importantly, yoga did not mean “yoke” or “union” in its classical usage, despite what most yoga teachers and popular writers on yoga say today. But, as many contemporary scholars of Indian philosophy will point out, it would indeed be odd for yoga to mean something like “yoke” or “union” since the objective of Patanjali’s yoga, as it is laid out in the Yoga-Sutra, is for the yogi to recognize and realize the true nature of the universe – i.e. that pure consciousness (purusa) is distinct from mere matter (prakrti), which includes our minds and our thoughts. In other words, the yogi does not seek union or oneness with the world; rather, he seeks to liberate himself from his attachment to the worldly.
And I would respond that to distinguish consciousness (spacial mind and qi) from matter (body mass and ideas) is simply a returning to our original nature. I would tend to describe our original nature as a functional order rather than a "union" since "union" is really a matter of perspective--whether we call it one, two (one 'yoked' to one) or three (one yoked to two) really depends where "we" are standing. Does "our" original nature really have any fixed limits? Sounds like liberation to me!