Sure, they're related, but they are not equivalent and even oppose each other in some ways.
A society that emphasises wealth accumulation above all else will have the privileged accumulate so much wealth it'll be nearly impossible for the poor to catch up, no matter how talented or hardworking.
One way of measuring class mobility is looking at your liklihood of finishing your life in a higher 'class' (variously definied) than you started it, or than your parents had. With that kind of measure, Sweden does extremely well. Certainly much better than countries like the USA, which arguably do emphasise making the accumulation of wealth (when you already have a lot of it) easier.
