“Power source” is a vague term. It really only means that all the power connections are not wired in common (even though they may be electrically connected). A single battery could be split out into multiple “power sources” due to having voltage regulators connected providing multiple voltages to different parts of your circuit. Sometimes the phrase is used to mean “power connections” where you may have two parts of a circuit powered by the same 12V battery, but there are two separate power connections to that battery: one for high current and the other for lower current.
Am I missing something? Or there are tweaks that will just make it works with just one single power source?
Yes, there are “tweaks” but you need to understand quite a bit of electronic circuit theory in order to do this successfully. Look up topics under the general headings of “power supply decoupling” and “ground loops” if you are interested in learning how to go about it.