The control rating deals with individual pitches, and the control rating you see in the players card is just an amalgamated stat from all of their individual pitch control stats.
A pitches individual control rating actually DOES have an effect on the control of other pitches, same with velocity and break. The overall control stat is a great reference for figuring out how much control in general a pitcher has over their pitches.
I use pulse pitching so I'll use it as a reference in order to show the factors effecting control.
One factor is how small the pulse CAN get. The smaller it can get, the more precisely a pitcher can throw a pitch. I believe this is the factor that control effects the most. You'll notice that no matter how high you make a pitcher's control, some pitches will still have a wider circle like curveballs.
Another is how often the pitch will actually be thrown inside the circle. I'm not sure, but I believe THIS is the stat that BB/9 effects the most. In theory, a pitcher with high BB/9 will throw within the circle more often, preventing wide misses and meatballs down the middle.
The third is how generous or tight the timing window is in order to get that circle as small as possible. This has a lot to do with pitch confidence and clutch.
All of these factors combine in order to determine pitch control. I may be mixing up BB/9 and Control, it's been a while since I figured it all out, but I hope I've convinced you the importance of having both, since they both have a huge impact on where the ball eventually ends up.
PS, I've made a max control, max BB/9 pitcher before. The difference is noticeable, but it's still not perfect. It is absolutely impossible to have a pitcher who places their pitches exactly where they want every single pitch. Also keep in mind that the faster a pitch is, the harder it is to control. Same with movement.