Analysis of a primitive often times is conducted on a reduced strength variant of the actual algorithm. This makes it easier to find the weak points of the design, which can become obscured after many iterations.
Assuming a "regular" collision means a collision over the entire 80 rounds, then a 76-step collision finds a collision after 76 rounds.
The paper for the result in question does mention that it is for a free-start collision. As for what this means, there is a Q/A here that does a goob job of explaining. Basically, it means that the attacker is allowed to select the initialization vector.