The offline "career mode" is your race history: best laptimes, best finish for each track/car combo, # of pole positions, wins, etc
The progression of your career (offline) combines those things with raising the AI difficulty, length of race, rules used and assists used, with the ultimate goal being (hopefully) to consistently beat the AI at max difficulty with full rules (or the real world rules depending on series) and no assists.
Online career progression is similar, granted you start with more manageable cars and keep your expectations realistic; you WILL be a backmarker when you start. Without practice, you'll continue to be a backmarker even longer. With proper practice you'll improve, but not everybody can be Jim Clark, but nearly anyone can be a competent driver.
You may always be a backmarker, but the goal should be to gradually get faster through consistency and improved racecraft. It's not about being the best, someone will always be faster.
Lastly, your "story mode" is the actual interaction with the sim racing community...sharing or withholding setup tips, beef with other drivers, admins ("marshalls") who rain down praise or punishment depending on your actions on and off track...seriously, who needs an artificial story mode when we have you wild, crazy and opinionated lot to argue with 24/7/365?!
rFactor 2, AMS, iRacing et al have story modes...it's called forums.