How we change what others think, feel, believe and do
A dog is stimulated by a passing butterfly and rushes off to chase it. It does not respond to your cue of calling it back (so your call is not a sufficient stimulus).
A child does not want to go to school. A parent offers to take them out for dinner afterwards if they go without complaint. The child reflects on this and agrees to go to school.
The intensity of a stimulus affects how a subject response. In effect, an intense stimulus is a different stimulus to a gentle one. A common approach when a stimulus does not work is to make it more intense. This may work, but it may also just confuse. There also may be another cause of non-response, for example speaking slower and louder to a foreigner will not get them to understand your language. When intensity increases, you can also cause a fight-or-flight reaction, which can be highly problematic.
A reward that is given after the action is not a stimulus. A potential reward that is shown before the action and to which the subject responds is an anticipatory stimulus. Anticipation can also be a response to a prior stimulus, such as 'sit'.
Reward is a desirable stimulus. Threat is undesirable. Subjects are usually attracted by desirable stimuli. This can have a particularly strong Pull effect if they cannot quite access it, such as when food is offered but not given. Undesirable stimuli has a push effect and can be more unpredictable, for example when it causes a fight-or-flight reaction.
In conditioning, a stimulus is provided in order to create a predictable response. With repetition, these become paired, with the stimulus always leading to the response. A cue is typically a stimulus that is deliberately created in order to trigger a desired action.
A stimulus is different from a cue by means of intent. A stimulus causes action of some kind (even mental, such as attention). You may provide the stimulus or not. The action may be desirable or not.
Once the stimulus has caused sufficient intent to act, it is no longer needed. It is a common error in conditioning to keep applying the stimulus even while the action is being completed (for example saying 'sit' after a dog has sat down).