Another point to add to Seth's:
Jewish communities have gotten pretty "mixed up" over time. Ashkenazic Jewry basically descends from the Italian communities of the early Middle Ages, and some historians trace them and their traditions back to the Jews of Eretz Yisrael (as contrasted with the Sephardim, who derive their traditions from the Jews of Babylonia). But the ancient Jewish communities of Eretz Yisrael were basically wiped out by the Crusaders, and the Jews who resettled it were largely Sephardim, especially after the expulsion from Spain. Hence the similarities between Spain and Israel.
(Something similar happened with France as well. Its old Ashkenazic communities were dispersed during the expulsions of the 14th century; the reconstituted communities of the 17th and 18th centuries were again mostly Ashkenazic, but most of them were lost to assimilation, and the rest were destroyed during the Holocaust; the bulk of present-day French Jews are Sephardim from North Africa.)
That said, there has been a fair amount of cross-fertilization too. You mention the Spanish Reconquista in your comment, and that indeed was part of what made it possible for Ashkenazic styles of learning (such as the methods of Tosafos) to enter Spain, and conversely, for Spanish influences (such as piyut) to travel north. Even earlier than that, though, the French Rabbeinu Gershom studied (directly or indirectly) under R. Hai Gaon of Babylonia, and conversely, the Italian "Four Captives""Four Captives" taught in Spain and other countries under Babylonian influence.