The simples explanation would be that Leaderboard is pure result based while Ladder is competition based.
More thorough explanation:
- It's basically a table that lists a result for a particular mode, stage, etc. often based around time (as in how quickly for time attack or for how long for endurance). For an example you can look at DiRT Rally, Project CARS, Asseto Corsa, DriveClub, it's nothing more than doing time attack mode to get best possible result for a stage in a particular car class. Therefore technically it's possible to never be beaten once you do a perfect run. Practically it's generally impossible, but the fact remains still. Also leaderboards don't promote actual competition, since you're spending more time driving alone than actually racing against other players. The worst thing that can happen to any racing game as it creates a highly "elitistic" environment.
- Ladder system is based on actual races/matches between the players. You're being matched with players of a similar rank to yours. Your position/stats at the end of the race/match determines how many points you get (there can be more factors, depends on the game). The more points you have, the higher in the ranking you are. The ranking can be divided into "divisions", so when you reach a certain amount of points you can do a race to go into a higher division. This whole process is similar to climbing the ladder, which is from what the name is derived from after all. Best examples of it can be found in League of Legends, StarCraft 2 or Rocket League. This style highly encourages direct competition between players which in turn makes the game a lot more populated and easier to get in. It also gives a higher sense of achievement, since you can be at rank 10 on Division 10, instead of rank 1240 as it would've been on leaderboards.
Generally speaking, leaderboards are for the "few chosen" who don't mind re-doing the same thing over and over again just to get as close as possible to a "perfect run". Ladder is more open and competition friendly since you're racing with people who will be of a similar skill while still being rewarded.
Naturally this is a very rough explanation, it's best if you check those games for yourself and how it looks. Leaderboards in racing games are usually very destructive to the community, while games that utilise ladders are being the most popular and successive titles out there. Makes you wonder, eh?