Do conditions under which players may enter them differ? Are there differences in the way points are calculated in the rankings?
The main differences are which organizations organize and operate the tournaments, how much prize money and how many points are up for grabs, and the rankings of the players in the draw.
Futures: Run by ITF, Prize money of 10-15k, ranking points from 1 point to 35, players ranked anywhere from 2000+ in the world down to about 150 or so.
Challengers: Run by ATP, Prize money up to 150k, ranking points from 3 to 125, players generally ranked higher though lower ranked players can still participate in qualifying draws. Not uncommon for top 100 players to play in Challenger tournaments.
Points earned at either type of tournament both add up to determine your total points and thus, your ranking. Some professional players spend the bulk of their career playing the Challenger series events and rarely ascend to the main ATP tour level events. A player like that would likely have a career high ranking just inside or just outside the top 100 in the world and would probably average a ranking of around 150-250 in the world.