I've got a Samsung Galaxy Smartphone with a USB 2.0 Type C charging port.
Using the stock Samsung wall plug (9 V, 1.7 A output or 5 V, 2 A fall-back) and charging cable (USB A to C) the device gets charged utilizing Samsung's "adaptive fast charging" technology.
They do that by going outside the USB spec. I'm making an educated guess here, as in educated by getting a BS in computer engineering and reading some USB spec sheets.
A common USB-A charger isn't technically "USB 2.0" because USB 2.0 is a data transfer spec, and a USB-A power brick isn't going to have much to say. They say what they need to by following the USB-BC (battery charger) spec, they have a resistor network across the data pins to specify being either 5 or 12 watts. Earlier USB-BC specs must have had other options as I've seen some "odd" power ratings on USB chargers before. Maybe the current USB-BC spec allows for more than just 5 watts and 12 watts but any USB-BC charger you see will be one or the other.
Using the included charging cable with a generic USB A wall plug without Power Delivery (5 V, 2 A output) nets a very slow charging speed of approx. 900 mA. Incidentally the same current as specified for USB 3.0 ports.
It is also incidentally the same current specified by USB-BC when the data pins are left open circuit. My guess is that the Samsung cable messed with the data lines in order to talk a Samsung charger into giving out more than the 12 watts allowed by USB-BC through a USB-A port. A USB compliant cable will not be tested for more than 5 volts and 2.4 amps, putting more than that through the cable could set something on fire.
The same exact charger and a regular Micro USB cable would charge any old smartphone with a maximum of 2A sans utilizing USB-PD. Why doesn't it work with the OEM Samsung USB A-to-C cable?
Without seeing the charger it's a guess that Samsung is using Quick Charge for delivering more power than USB-BC allows. It's likely an attempt to not get angry phone calls over broken cables and chargers that Samsung has everything Quick Charge fall back to the "safe place" of 5 volts and 1 amp.
The Samsung charger is going to look for a compatible cable and device before giving out more than 5 volts and 1 amp. The cable might have USB-A on one end and USB-C on the other but there's going to be something different about it than a USB compliant cable. One difference is that it will be built to take more than 5 volts and more than 1 amp. Another difference is there's going to be some means to tell the phone and charger it's a Quick Charge cable and not a common USB cable.
The USB 2.0 specification also states a maximum of 500 mA and every charger in the last years exceeded that. The Samsung device doesn't even have a USB 3.0 port, it's just USB 2.0 with a Type C connector.
The USB 2.0 spec requires a minimum of 500 mA to any port. A USB 2.0 device is allowed to draw up to 1.5 amps. But a USB-A charger is not held to the USB 2.0 specification, most comply with USB-BC.
Most USB chargers will be "dumb" USB-BC devices that use a resistor network on the D+ and D- pins to tell anything plugged in how much power is safe to draw. Current USB-BC chargers will be either 5 watt or 12 watt. Older USB-BC chargers had to be a minimum of 5 watts, and for the sake of backward compatibility that's why devices fall back to drawing no more than 5 watts.
I'm trying to understand this from a technical viewpoint. Can you point me into the right direction? USB 3.0+ and Type C is honestly pretty confusing.
It is confusing, and non-USB compliant devices and cables like what you got from Samsung is only making it worse. I'll try to summarize the distinctions between the different specifications for you.
USB-BC (battery charging) is a very simple specification for transmitting power. It's current iteration, version 1.2, allows for either 5 watts or 12 watts from USB-A to micro-USB-B or USB-C. Anything providing more than 12 watts from USB-A is not following the USB spec.
USB-PD (power delivery) allows for power to devices from 5 watts to 100 watts. Direction of power flow and voltage will be negotiated between the end points, and limited to what is safe based on the cable detected between them. USB 2.0 can be used to negotiate power, as can the configuration pins on a USB-C cable.
USB 2.0 is primarily a data transfer spec. People used this for power before USB-BC came along because it was a convenient way to get 7.5 watts for charging small portable electronics. Because USB-PD and USB 2.0 are often found on the same devices it's possible to see devices use USB-PD to supply more than the 7.5 watts allowed by USB 2.0 alone. The 12 watt limit still applies for anything other than USB-C
USB 3.x has all the same power limits as USB 2.0 to maintain backward compatibility. Like with USB 2.0 devices a USB 3.x device is able to use USB-PD to negotiate for more power.
Quick Charge is a specification that uses USB ports for delivering power. Since it complies with the USB spec only on the most basic level it will fall back to 5 volts @ 1 amp if there is anything not Quick Charge in the chain.