I guess the parent poster means that Rubik did not have an existing solution to follow, and his one month meant solving it without any external assistance.

(I'm not sure how his invention process went exactly, but I would guess that he probably did not start with a physical device he could hold, so I'm not sure such comparisons are really meaningful. It may have been easier for him to solve, due to inside knowledge, or it may have been harder.)

In the cube solving world, movement sequences that arrange the cube in a specific way are called "algorithms". Each "algorithm" will solve part of the cube, the full solution being a sequence of "algorithms".

It's the same thing. I just used a different word.