This distinction concerns whether or not the subject makes a bodily movement in order to attend to something.
One common measure of covert attention is inhibition of return (IOR): recently attended locations are less likely to be attended to again.
However, it's not clear that these are two distinct kinds of attention, as opposed to one kind that may or may not be supported by movement.
Moreover, there is evidence that overt and covert attention involve common brain areas.
Direct vs. Indirect Cueing
In the Posner spatial cueing paradigm, subjects are presented either with "direct" cues that appear at target locations, or "indirect" cues that appear at fixation.
There are significant differences in the forms of attention evoked by these differing cues: direct cues draw attention more quickly but for a shorter time, followed by a period of IOR. Also, only indirect cues are affected by cognitive load.
Top-Down vs. Bottom-Up
This is one basic distinction suggested by the Posner cueing paradigm: it concerns whether a subject's attention is influenced by "higher" cognitive processes.
Some examples of such processes would be intentions, semantic knowledge, etc.
Wu's definition (p. 30): S's attention to X is top-down if it involves the influence of a non-perceptual psychological state for its occurrence, and bottom-up otherwise.
Though we might ask: What kind of influence must this be? And how do we discover it experimentally?
Controlled vs. Automatic
Here, the specific issue is whether or not a person attends intentionally to something (under a certain description).
Note that this is not just a matter of attending as one intends, but also of attending because of this.
Thus Wu (p. 33): S's attention to X is controlled relative to feature F if S's attention having F results from S's intending it to have F.
Here again there are some complications: How must attention result from intention? And how is this to be measured?
Are there really two separate distinctions here?
Top-Down
Bottom-Up
Automatic
Controlled
Which distinction is revealed in the Posner cueing paradigm?
Wu's "Empirical Sufficient Condition"
S perceptually attends to X if S perceptually selects X to guide performance of some experimental task T -- i.e., selects X for that task.
The idea so far is that selection for a task is sufficient (enough) for attention, not that it is necessary (required) for it.
And this is supposed to be implicit in experimental practice.
Note a worry, however: How exactly can we make sense of this "in order to" language when automatic processes are concerned?