The fundamental character of money stayed the same, even if there were restrictions on it, as did the capitalist character of money paid through predominant wage labour. The state still collected taxes (perhaps at a different stage in the production process, though) in money. China also has currency controls, but the renmbini is just as much currency as the US dollar is.
Just as a crime exists in a country (albeit with practical restrictions, i.e. you get thrown in prison), money has existed in every modern country, even the so-called "socialist" ones, with some other restrictions.
The character wasn't the same, because money was not enough to buy you things. You needed special coupons to buy things, and coupons were distributed by the government using various systems.
So you could have enough savings to buy a new car/fuel/washing mashine or even meat, but unless you had a coupon the money gave you nothing.
For that reason for example used cars were sold for above their original price. You could buy a car for an amount, drive it for a few years, and sell it for a higher price than originally - but you wouldn't be able to buy a new one unless you had a coupon for a new one.
The same with fuel or meat. You could have a ton of savings, but unless you have a coupon, you wouldn't be able to buy meat or fuel to that car.
The coupons were distributed by the government through government companies.
Due to shortages many basic products were rationed and you simply couldn't buy them with cash. Having more money didn't make a difference unless you had the right rationing stamps (or connections to a high-ranking party official). This lead to a whole secondary market of people trading stamps with each other (e.g. cigarette stamps for meat stamps). When it comes to accumulation, periods of hyper-inflation and lack of investment opportunities made this much harder. Moreover, currency exchange rate was controlled by the government, which led to illegal underground currency trading.
This is based on experiences from Poland, but I'm sure many other communist countries had similar issues.