All human Y chromosomes descend from one ancestral person. Since they all descend from one person and then from a few families, and as times goes by those families keep branching out up to the point where we get to our own family nest, it would be natural that when we compare our DNA, the fewer markers we compare, the less unique they are, and the more markers we test, the more unique the whole string of markers is. In other words, to go to extremes, if we tested only one marker, we would most certainly match with millions of individuals that shared that marker for thousands of years. But if on the other hand when we test many markers, we will match very few people that share those same markers. Those would be the ones that are closely related to us.
This is valid when comparing our matches on 12, 25, 37, 67 or 111 markers. The likelihood that we will match other individuals with 12 markers is far greater than matching on 25, 37, 67 or 111. Especially if our family descends from a populational group that came from one or a few prolific families thousands of years ago (which is the case for Western Europe). Dr. Luigi Lucca Cavalli-Sforza, Professor Emeritus, Stanford University, in his fascinating book: The Great Human Diasporas: The History of Diversity and Evolutions says that the total population of Europe was 60,000 people at the end of the last Ice Age, about 10,000 years ago. Now Europe has a population of 300 million people. This increase is almost entirely due to a natural increase in population rather than immigration from other continents. Keeping this in mind it is reasonable that many people alive today in Europe will match with other Europeans from BEFORE the time that our ancestors began the adoption of surnames, and when you match someone who has a different surname your first thought should be that the ‘connection’ is distant rather than recent.