I understand that circuit boards receive a positive current from the battery pack and basically distribute it to different circuits on the board. I understand that whatever we program into the controller chip of that board will determine when and how current will flow.
However on this board I have which belongs to a hot wheels car that I bought a long time ago there seems to be many grounds and also different looking points of connection for example in the middle of the board you see that the first four are basically holes labelled from P00 through P02 and a GND, whereas the next few points of interconnection look like they have a wire actually soldered on to it. I have tested these with a multimeter and all of those connection points P0 zero through P whatever perform different functions and they work.
I wanted to post the image but I can't.
My basic question is why do those points of interconnection look different in the sense that some of them have a soldered wire and the other ones just have a hole?
Well, not knowing what you're looking at, it's hard to say.
I'm assuming when you say hole, you just mean a hole + pads in the circuit board, not a female connector.
One reason you'll see multiple grounds is that everything connected to the board is going to need it's own ground wire. Typically, for hopefully obvious reasons, designers locate all the pins going to a specific connected device near eachother, usually in a row for some kind of connector (though cheap boards often just solder wires directly on).
as for unused points of connection, the cost of having PCB's fabbed is a function of the number of boards of a given design you're making, the size of the board, and the parameters (coating, how tight a tolerance you need, what substrate, etc) you want on it. Thus, if you're going to be making a bunch of similar things (say, a bunch of different toy cars with different assortments of lights or whatever), it's cheaper to just make one board that can handle the fanciest one you plan to sell, and use that in all the models, with some of the connections unused.
Marciokoko:
I wanted to post the image but I can't.
Well, you will need to in order for us to get any sense out of it. Both sides of the PCB.
If you have a perfectly focused photograph - and I do mean that - lodge it on a proper site - I think "Imgur" is one but many others are no good - and use the "Insert an image" icon, the little "screen" with a "+" in its corner - to post the link.
(To get a focused photograph, use a real camera, take the object outside in daylight but not in the sun. Unless you are skilled with its "macro" function, use the camera at least a metre away with maximum zoom. Then reduce it to a resolution which fits on the screen - generally less than 1024 pixels wide.)