Whether this is a make-up for the first, a time-extension of the first, or a Offering of its own; the difference being where one was exempt from the First but not the Second: Pesachim 93a-b, Chagigah 9a-b
One who converted after the first Pesach and before the second one: Pesachim 93a
One who became an adult between the first Pesach and the Second: Pesachim 93a
Requiring Removal of the "Name" of the Offering to make the original Offering Pesach into a Celebratory Offering, even if it is brought at the wrong time: Pesachim 64a
Whether one receives the punishment of Divine Ex-Communication for missing the first Pesach, first and second, or just the second: Pesachim 93a-b
One who was Uncircumcised, or Impure, for the first Pesach
The Second Pesach is brought by one who was Impure for the first one: Pesachim 92b
One who had the opportunity to become pure, or to be circumcised, before the first Pesach: Pesachim 94b
One who was "Far Away" for the first Pesach
Second Pesach is brought by one who was "far away" for the first one: Pesachim 92b
Defining "far away" as either 1) A distance from which he could not arrive by the time of Slaughtering/Consumption of the Offering, defined as being beyond the radius of "Modi'in", or 2)Anywhere outside the External Room of the Temple: Pesachim 93b, 94b
If one was "Far Away" but could make it with a fast animal: Pesachim 94a
If one wasn't "Far Away" but was kept away by traffic: Pesachim 94a
One who could have arrived in time: Pesachim 94b
One who Was eligible for the first Pesach
Second Pesach is brought by one who was kept from doing the first Pesach by unavoidable circumstances: Pesachim 92b, 93a
Second Pesach is brought by one who was kept from the first Pesach by human error: Pesachim 92b
One who intentionally missed the first Pesach: Pesach 93a