The answer to this is mostly a matter of defining the words involved.
Acetylcholine is a chemical that acts as a neurotransmitter. This means that there are cells which are capable of recognizing acetylcholine, and performing an action when they recognize it, without conscious effort. Many drugs and diseases involve manipulation of this mechanism.
Agonists are one such manipulation; they are chemicals which bond to the receptors. They may be the "correct" molecule, or something else that's similar enough that the receptor can't really tell the difference. The receptor accepts the agonist molecule and then fire their signal, so that the body acts.
Antagonists are very similar; like agonists, they bond to the receptor site, but they do not allow the signal to fire. Instead, they just clog up the receptor and prevent it from firing its signal at all.
Seizures are basically an uncontrolled muscle spasm, and paralysis is a loss of muscle control. Thus, comparing these definitions, we can see that an agonist would cause seizures, and an antagonist would cause paralysis. Therefore, black widow venom causes seizures and botulism causes paralysis.