Im having a hard time understanding how distinguished points (DP) work. From what i know you only save the start point, trail length, and DP per a trail and start a new trail when a DP is found. You repeat this until you find a collision DP and some how find the "actual" collision of the pubkey.

I don't understand how finding and only storing DP would lead to finding the pubkey collision. I fully understand how the kangaroo method works by creating 2 maps to find a collision using the birthday paradox. but I'm not sure how you can do this without storing the whole set a points.