In regards to ethical positions, what is anti-teleology, and how is it different from deontology? Are they opposites or is their relationship of another sort?
The difference is simple.
Ethical positions that evaluate the consequences of action which determine right and wrong are considered teleological. Ethical positions that hold that there is a duty to behave in some way are deontological. Thus, someone who rejects the former is anti-teleological, but needn't be deontological. For instance, one might reject consequentialism with anti-teleological sentiment but be a situational ethicist.
From EB's article on teleological ethics:
teleological ethics, (teleological from Greek telos, “end”; logos, “science”), theory of morality that derives duty or moral obligation from what is good or desirable as an end to be achieved. Also known as consequentialist ethics, it is opposed to deontological ethics (from the Greek deon, “duty”), which holds that the basic standards for an action’s being morally right are independent of the good or evil generated.
As all things philosophical, often philosophical discourse ranges around what an ethical position can be characterized as. Consider the SEP article on Kant's "Moral Philosophy".
The received view is that Kant’s moral philosophy is a deontological normative theory at least to this extent: it denies that right and wrong are in some way or other functions of goodness or badness. It denies, in other words, the central claim of teleological moral views. For instance, act consequentialism is one sort of teleological theory. It asserts that the right action is that action of all the alternatives available to the agent that has the best overall outcome. Here, the goodness of the outcome determines the rightness of an action. Another sort of teleological theory might focus instead on character traits. “Virtue ethics” asserts that a right action in any given circumstance is that action a virtuous person does or would perform in those circumstances. In this case, it is the goodness of the character of the person who does or would perform it that determines the rightness of an action. In both cases, as it were, the source or ground of rightness is goodness. And Kant’s own views have typically been classified as deontological precisely because they have seemed to reverse this priority and deny just what such theories assert. Rightness, on the standard reading of Kant, is not grounded in the value of outcomes or character.