My attempt at TL;DR: SHA-1 works on blocks, and each block is processed and it's data "mixed" with a previous intermediate result based on the previous blocks (Merkle-Damgård construction). A freestart collision only shows blocks and values for the intermediate results which lead to a collision. For a full collision you still have to figure out what sequence of blocks gets the intermediate results to the necessary values.
It looks like the did the same thing or something similar in 2^57.5 SHA1 calculations back then versus 2^63 SHA1 calculations this time.