In order to answer as best I can, I'll have to be a bit picky with the term "capital" as you use it here. Capital isn't just the means of production and distribution, it's MOP and MOD employed essentially to pilfer surplus value. This is called "valorization" of capital, where the capitalist "casts out the net of money, returning back to his pockets more money," or mathematically expressed, the M-C...P...C'-M' process (where M is money, C is MoP and labor-power, P is production, C' is the produced commodity of higher value than what C was purchased for, and M' is the greater sum of money that becomes the new M).

All of that is important because this process is the general path of capitalist accumulation, that works out only because capital owners own capital. This circuit is where profit comes from, which has tremendous impacts on the structure of the state, the distribution of wealth, and how power itself is distributed. It creates an owning and a working class.

To return to your actual question, what's the difference practically for administrators in a socialist state or communist society (at which point in development there are no classes and thus no need for a state, but that's me being picky with terms again)? The difference is that management of production and distribution is not the same as employing it for personal profits in that same circuit described earlier. In capitalism, managers and CEOs are rarely owners of capital, but merely servants of the actual owners (though owner-managers do exist, of course). Management is socially necessary labor, especially in highly advanced production, but ownership creates not one bit of value itself, as I'm sure we agree.

This is why I say that the problem isn't that production is managed with intra-class hierarchy, but instead the form of the superstructure. Socialist states aren't perfectly democratic, because they exist in the real world. The measures we put in place to advance democratization are organizational structures that are vital to constructing more effective socialist management. Council/soviet democracy is one such example, where local and regional committees elect delegates to higher committees. Protections against corruption can come in the form of recall elections and frequent elections, and education itself on how the system works and bringing the people up into the system with mass participation also helps.

Administrators are not magically immune to corruption, of course. We have to learn the best structures through testing theory to practice. Socialist democracy has gone through many changes over the years, and each socialist state that exists today has its own form, even if they may share characteristics. The important takeaway, though, is that because administrators in socialism do not actually own capital, but merely direct and steer production, they do not participate in a circuit of accumulation for their own profit.

They can abuse their power, but do not form a class, and thus share the common class interest with the rest of the working class: develop the productive forces to a level where they can be fully collectivized, and run to a common, scientific plan. Both administrative workers and non-administrative workers share this interest, as it benefits all, and this process naturally requires greater participation by all in the running of society simply to keep up with the advancing complexities of production and distribution. This has an equalizing effect and erodes the distinction between administrative and non-administrative labor.

This was a bit of a ramble, but I hope I made sense!