Also note there are "private" groups dedicated to certain play styles. Most of the powers (Mahan where I'm pledged) has a private group where the only humans you will encounter are your own power.
We use this to construct wings to accomplish certain power tasks and answer question concerning strategy and tactics.
There is also "Mobius" where there is a very large mix of players of all styles, powers and intents unified by their promise to only shoot NPC. This is a good way to get your feet wet toward Open mode.
As mentioned, Private, Solo, Open all play in the same universe which is maintained by the servers we all connect to regardless of play mode.
When you exit Hyperspace, enter/exit Supercruise, enter a combat or Res zone, enter a station, trade, etc., each trigger communications with the servers to synchronize your universe with everyone else.
On an on-going basis (open/private) your computer is constantly sending/receiving positional data (match making) to determine which human player(s) get connected to you via PtP to see, communicate and enter combat with or against each other.
Any actions which affect the economy or politics of your world, also affects the open world and the other way around. This keeps the universe for everyone dynamic and allows you to switch modes to see what you like best, or fits your mood at the time without any noticeable changes to your ship, economy, politics, relationship to NPC, or your friends.
This also has the effect when pledged to a power, you can help or hurt your power regardless of the play mode, so even if not playing in a human environment, I encourage power players to keep in contact with your power's reddit, Frontier Power Play pages and/or voice chat to cooperate most effectively with faction (or "fraction") goals rather than being a counter productive fifth columnist.
If the layered subtleties of Power play baffles, join the club. The screens the game presents containing power specific information is often confusing, conflicting or totally inaccurate. Being in communication with other power players will help tremendously toward making a useful sense of it.
-Pv-