A lurking variable doesn't just affect the apparent relationship between two variables. An interaction term might do that but wouldn't be lurking. A lurking variable directly affects both X and Y and thereby makes it appear that X and Y are directly related to each other when, without the lurking variable, they would not be or would not be to that extent or in that direction.
My favorite is the strong positive association between the number of firefighters at a fire and the amount of damage. Perhaps you shouldn't call the fire department. The lurking variable is the size of the blaze, which "causes" both damage and fire fighters.
It isn't necessary for lurking variables to be unobserved. Often they are lying around in the open in the data or available in related data. It is their joint affect on two variables, creating the spurious appearance of a relationship that makes them "lurk". The best lurking variable stories hint at spurious causation: storks "causing" births, firefighters "causing" damage, TV's "causing" greater life expectancy, and so on. But cases where we actually had a right to conclude causation are rare because they would only show up in the context of a designed experiment and that would mean that somehow the randomization had broken down. So often lurking variable examples are cautionary tales warning us not to infer causation from correlation.
Confounded variables vary together so that one cannot tease apart which is responsible for any observed effect. But only predictors (or factors in an experiment) are said to be confounded. An external variable that is correlated with our response, but not associated with our factors is not a confounder because we will still be able to observe the effect of the factors on the response. Confounding can occur due to poor design in an experiment (offer both a low interest rate and low fee to one group of customers and a higher interest rate and higher fee to another; you'll never be able to tell whether customers were more motivated by the difference in interest rate or the difference in fee.) But confounding can also simply be structural. Any study that takes place over time risks that something else will happen during that time that will vary with the treatments and could be responsible for the observed effect -- but we'll never know. Confounding is related to collinearity in linear models. In both, we can't separate the effects of two (or more) potential predictors because of the structure of the data, but there needn't be any particularly strong association with the response variable.
So, a hint: lurking variables are most common in observational studies. If we are *observing* two variables over time, for example, then an external change (seasonal, political, economic, or whatever) could affect both of them and thereby be a lurking variable. They are much less common in designed experiments because we randomize to avoid such things. Lurking variables will show up only if we fail to randomize completely or correctly. If we are *controlling* a treatment and observing a response over time, an external change wouldn't lurk because it couldn't affect our treatment variable.
Confounding, however, can show up in an experiment either through poor design or just because there is no reasonable way to avoid it. Things happen that are not under our control, but might be confounded with the factors, making it impossible to tell whether our treatment or the external change was responsible for the response. The best defense is to record as much supplementary information (temperature, precipitation, economic conditions, whatever might matter) so that these could be used as covariates in our analysis. Even that might not cure the problem because the external variables might still be collinear with our factors and impossible to separate from the predictors we care about.
(Of course, the concepts of multiple predictors, covariates, and collinearity are beyond the scope of the AP syllabus, which is probably part of what makes these topics confusing here.)
---- But in the final analysis (as it were), it really doesn't matter what we call them. The important thing for students to recognize is that variables other than those named in the study may be closely associated with one or several variables. When we learn about a study, we should be skeptical and think about possible external variables. When we find (or think we may have found) some, we must take extra care in interpreting the models, and we should be especially cautious about inferring causation. If differentiating lurking from confounding variables helps students to understand this, then go for it. But if it becomes just another trivial distinction for them to memorize then I say to hell with it. Focus on what happens to the models and how to interpret them with care when other variables might affect the data.