Lord Kilo Von Mortenson
A goal of Taoists is to become one with the Tao. To move, act, speak, etc, with the Tao. This is not to say they communicate with the Tao, but rather that they allow the Tao to flow through them in their actions. This could also be considered simply doing, or as the Tao Te Ching describes- doing not doing.
(Old Post I know, but I couldn't resist I tell you!)
Words are so fun aren't they? The Tao te Ching opens with 'the name that can be named is not the eternal name' while Chuang Tzu expresses 'words exist because of meaning; once you've gotten the meaning you can forget the words.' It is always key when dealing with Taoist ideas to remember specifically that, that words are more meant to 'point' in the right direction than to be absolute statements. The Taoist recognizes that is the meaning behind words that bears the fruit of thought, words are just a tool of conventional language meant to share those ideas but should never be taken at face value or for the value of the word itself. (Etymology and grammatical content in relation to any discussion in Taoism is therefore like a dog chasing it's own tail. The dialectic so popular in the western world when approaching foreign philosophy is naturally self-defeating.) Always important to bear in mind in any discussion involving Taoism.
An interesting place to draw parallels here to Taoism would actually be to the Vedic traditions before Buddhism, specifically the idea of Brahman versus the Tao. (I can only imagine what the dialogue between Taoism and Hinduism versus Buddhism would have given birth to.) 
In many Vedic traditions, it seems the idea is to express a thought in such a mythological content that it would be absurd to take it as literally. In this case, in this case the idea is that the supreme cosmological being 'Brahman' constantly puts on a play in which it divides itself and is all the characters. Brahman, through the spell of maya, forgets it's original identity as it becomes absorbed in all it's various roles. We in the conventional reality take the 'play' to be our true reality and so forget our original identity or self, the 'atman' which is part of the one Brahman. The spiritual tradition is to remember the 'atman', to become aware of our true Brahman nature and to eliminate the false idea of 'ego as self'.
Taoism on the other hand doesn't seek to establish any sort of direct mythology as Hinduism tends to. Tao is similar to Brahman in that it is a supreme cosmological being, an all pervading-reality and sense of 'one-ness'. To give the all-pervading sense of Tao one does not say that Tao is divided in mythological context but instead points at all the things convention does not take to normally be valuable. The Tao te Ching refers to it as lowly and feminine. Chuang Tzu says it is in the piss and the s**t. The Tao creates and begets the myriad forms of existence, but does so in a completely non-personal way. One might compare this creation process to reproduction to avoid confusing it with the Judeo-Christian idea of creation: When two people engage in intercourse they 'create' an offspring but do not choose specific traits to be given to that offspring. Without the parents knowledge certain traits or aspects of self are at random picked from each and imparted upon the child, which then 'grows' into it's own being. 
The spiritual tradition of Taoism is in a sense similar to Vedic traditions in that one must 'remember' the unity with Tao, the sense of oneness prior to the idea of the conceptual self. However, unlike them there is a strong emphasis on spontaneity and 'intention with no intention' or 'pure intention'. Hinduism seeks the atman while the Sage forgets there is a self to seek in the first place and allows their true nature to act as it will.
I make these comparisons because wu wei is a very difficult concept to grasp, comparing the spiritual practice of the Hindu to the Sage I hope points in a different direction than others are used to and may help paint the picture of wu wei a bit more. Indeed the idea of 'grasping' wu wei is loosing it, as wu wei is letting things be, letting go, the lack of grasping, understanding but simply action without contrivance. Wu wei leads naturally to te (virtue that has no intention, that is not virtuous for the sake of being moral or virtuous), both of which are key behaviors for the Sage. 
Taoism and Buddhism got a long so famously because much of Buddhism seemed to ring parallel to wu wei, to share the same idea in a different way through the art of letting go of attachment and desire, recognizing 'void' and suchness' and the idea that the 'ego' has any bearing only because we make it so in our own minds. Compassion and loving-kindness share traits with te as well. 
The contrasts between the two aren't so much in the basic ideas behind scriptures for either one because the underlying idea expressed by the words is inherently the same. The one whom achieves nirvana essentially behaves and views the world similarly to the one whom becomes a true Sage. The contrasts are more in the approach and the idea of how to approach enlightenment and sage-hood, respectively. In Buddhism one is guided by precepts, a set of behaviors (or lack from) that are generally agreed upon to lend themselves towards enlightenment. One disciplines the mind through meditation and becomes aware of the nature of it and the true self rather than the collection of memories and 'ego' we often take to be the actual self.
Taoism on the other hand doesn't really tell you a thing! It has plenty to say about what not to do, about the usefulness of the useless, of the creative power and use of emptiness, it has plenty to say about 
not doing but almost nothing to say about what 
to do. Why should it? Why should one just mimic the teacher and expect to find sagehood in the mimicry when sagehood is no where to be found in such action, that sagehood is attained through a sense of genuineness in which one is not separated from their actions, but experiences no separation from them and indeed is them. The action that is performed because it is 'discovered' rather than shown has more that sense of genuine, true nature that the Taoist seeks. 
And here is where Ch'an and Zen are born. Zen is still Buddhism, it still has the same core and aim as the rest of the Buddhist world, but unlike much of it it takes the Taoist emphasis on negation and personal discovery rather than teachings, doctrine, and guidance. Koans do as much of the Tao te Ching and Chuang Tzu does and express the limits of language and logic, of contrivance in thought. One must discover Zen for one's self. 
If you relate the experience of enlightenment, satori, and becoming a sage to a traveling man trying to find a specific town, the Zen or Taoist master only tells you when you're going the wrong way and will make no effort whatsoever to tell you the right way. The conventional ego for this reason finds him most infuriating. He will even obstruct your efforts of finding the right way in order to force you to see all the aspects of conventional thought and behaviors which are keeping you from naturally finding your destination, some of which are so subtle that they'd be extremely difficult to identify otherwise.
All of this mainly served to expand the idea of wu wei and add to it. Such a general picture glosses over the flavor of it that is essential to an understanding of Taoism and where most of the comparisons and contrasts between it and Buddhism exist. (And what makes Zen so different from other forms of Buddhism.) I'd take on other parts as well but as I stated in the beginning, the dialectic naturally defeats itself in a Taoist discussion. ; )