Tosafos explains that anytime a veset is dependent on a specific day such as a date of the month (15th nisan, 15th iyar, 15th sivan), the veset is established after 3 times. But anytime the veset is dependent on the passing of a certain amount of time such as veset haflagah where she creates a veset to see every 36 days, it must be 3 times of 36 days passing which would require 4 times seeing blood.
In the mishnah we find that an animal can become a mu'ad for shabbos and remain a tam for the duration of the week. Can an animal become a mu'ad for tuesdays? Rashi and Tosafos imply that an animal cannot become a mu'ad for a specific day of the week because they offer specific rationales to explain why an animal can be a mu'ad for shabbos (rashi - no work, tosafos - special clothes). They seem to understand that there is nothing special about an ordinary day of the week that we can attribute the goring to, therefore, only on shabbos where we can associate it to the actual day, would the animal become a mu'ad after just 3 times (similar to becoming a mu'ad for yom hachodesh). But, if the animal will gore on tuesdays, there is nothing special about tuesday that would make it gore, so it would not become a mu'ad until it gores 4 tuesdays in a row and creates a chazaka to gore every 7 days, starting from tuesday (similar to a veset haflagah).
Tosafos assumes that goring every other day, is similar to a haflagah, just a very short haflagah and would require 4 times to create a chazaka. Tosafos draws a distinction between goring every other day and goring every other animal, because by goring every other animal it only takes 3 times to make a mu'ad. Tosafos seems to understand that goring every other day is similar to a haflagah where a woman would see blood every 36 days, so it will take 4 times to create a chazaka. But goring every other animal would be similar to a woman becoming a nida on (15 nisan, 15 sivan, 15 av), where she skips a month, but nonetheless the seeing is attributed to the day and therefore only takes 3 times to create a chazaka. Here too, although it skips animals, the goring is attributed to every other animal that it sees, so it only takes 3 times to create a chazaka.
In all the above cases, Tosafos assumes that Rav and Shmuel would agree (not like rashi who says that they argue about the goring every other animal that it sees). Tosafos understands that the machlokes rav and shmuel is only when the seeing of nidah is attributed to the day of the month, but it is with a di'lug - skip, such as 15th nissan, 16th iyar, 17th sivan. Even though all agree that a haflagah can only be determined after 4 times, in a case of dilug there is a machlokes.