Definition of the fallacy "two things with an anecdotal similarity are treated as equal, but the claim of equivalence doesn't bear out because the similarity is based on oversimplification or ignorance of relevant additional factors".
This fallacy is at the core of many of the other fallacies, and other fallacies have been created to reinforce the truth of this one.
Example 1
On April 30, 1975 the fall of the city of Saigon marked the end of the Vietnam War and the start of a major refugee crisis. Millions of Vietnamese people fled their homes looking for refuge and freedom and many tried escaping across the South China Sea in small leaky boats.
Two distinct events are quietly made into one by placing a reference to the fall of Saigon next to a reference to the boat people crisis, without further comment as to the similarities and differences between the two events. The fallacy is in not pointing out the differences between the two events that are relevant to the discussion at hand.
This fallacy is used to pick out characteristics from either event and attribute them to all of the Vietnamese refugees in Canada. For example, they are all victims of the fall of Saigon (the first event only), or they were welcomed to Canada in large numbers (the second event only).
For example, we often hear that since the fall of Saigon caused the refugees to come to Canada, we can make an homage to the refuges with an homage to Saigon. One of the differences not pointed out is that the boat people came from all over Vietnam, with probably a majority coming from the north. With that knowledge, one realizes that the homage idea is actually a political attack on the boat people, not an homage.
Another relevant difference is the very different approaches that Canada, the UNHCR, and the world took to dealing with the two events. In particular, no one was admitted to Canada for the sole reason that they were a victim of the fall of Saigon because they were not UNHCR refugees.
The originator of this quote might defend it by arguing that some of the victims of the fall of Saigon left in small leaky boats. They did, but the key word making it a reference to the boat people crisis is "millions". Less than 200,000 left after the fall of Saigon, not all left in boats, most that did were picked up offshore by US military ships, and a very, very small fraction of those ended up in Canada. The number of boat people comes much closer to "millions". The whole point of the fallacy is to equate the boat people, who were welcomed into Canada, with the Saigon elite, who were not welcomed into Canada in large numbers.
Like nearly every example on this page, this is also a persuasive definition fallacy (dog whistle). The former boat people will understand this as a lowering of their legitimacy in Canada: because they did not come from Saigon, they are not being recognized. Their identity has been stolen.
Discussion
This is by far the most common fallacy because this example appears in some form in every political statement and press release, and in any mention in the media about the Vietnamese in Canada. The quote above is from bill S-219, so it is reiterated every year in Journey to Freedom Day (the name of the day itself being a persuasive definition fallacy).
This fallacy is also the basis for other fallacies, such as the illustrations shown for 'appeal to emotion' and 'affirming the consequent'. This fallacy is so fundamental to the political agenda, that other fallacies have been created to reinforce the truth of this one -- see the illustrations for 'appeal to authority' and 'faulty generalization'.