Are logic gates, one shots, truth tables, etc consistent across all manufacturers or are there sometimes variance among them?
Knowledge of Digital Logic underpins knowledge of Digital Electronics, but in practice you have to understand more than just the basics. the reference to "our logic works on falling edge," is almost certainly a reference to synchronous digital design, wherein for the most part, unclocked or asynchronous logic is frowned upon and/or otherwise abstracted away from your concerns as a designer.
Do you know what I mean when I say "synchronous digital design?" Do you know what an "edge triggered flop" is? What about different CMOS vs. TTL vs. ECL logic? The concepts of Digital Logic are the fundamental building blocks upon which almost all understanding of electronics rests, but knowing truth tables may or may not be enough, depending on whether you are doing VLSI chip design, FPGA design, Embedded control system design, or what have you. Underneath those ones and zeros are voltages, currents, charges, resistances, inductances, and capacitances.
1 AND 1 equals 1 but (CMOS 1) AND (PECL 1) almost certainly doesn't equal (CMOS 1).
If you are learning out of necessity, I would just continue down the rabbit hole. The vast amount of practice in the electronics domain forbids one from "knowing everything" and demands that you tinker and learn what you need to know today, try to reuse it tomorrow, but recognize that something new is almost certainly going to pop up.
I don't know what your area of expertise is, perhaps software (as you went in via API/Guis)?
Consider a communication stack, with the lowest layer being the transmission of bits, and higher layers establishing networks, guarranteed delivery, and yet higher layers doing something useful at the app level. Few designers would work over more than a few levels, and then not at the same time. The point of layering is to reduce the context you need to do useful work.
Digital electronics has a broadly similar layered structure. Within the chips are transisitors, then gates. Small ICs might provide just these function, but they can be built into bigger ICs, providing higher level functions like RAMs and multipliers, which go into DSP devices and SoC devices. These are so complex, that to use them, you have to abstract out the interface as perhaps registers (the lowest practical level) or messages, or an operating system. Again, attempts to work on or understand more than the current layer, plus the ones above and below for the interface specification, may be doomed to confusion.
Recognise there is a some sort of layering hieracrchy (it's nowhere near as well defined as for instance the 7 later OSI comms one), when you get some information, try to figure out what sort of layer it's about, then try to figure out the interfaces up and down one level.