Sorento PHEV modes, explained
It wasn't until I'd had my car quite a while, and experimented with settings, and revisited the manual, that the attributes of drive mode and hybrid mode became well formed in my mind. Here is my summary of how it works.
These notes pertain to the 2022 Sorento PHEV. Much of this will still be true for later model years.
Drive Mode
The main purpose of drive mode is to determine acceleration responsiveness and power, which influences MPG. You set drive mode with the twisty knob on the console.
There are four drive modes: Eco, Sport, Smart, and Snow.
Eco is the default. In this mode, acceleration response is slower. Surprisingly to me, it can also reduce the A/C performance, AND the responsiveness of smart cruise control. So says the manual.
Sport mode provides the acceleration responsiveness that you'd expect from the name. The engine runs constantly. Sport mode will also recharge the battery. For example, I went from 8% to 28% charge in about 10 minutes of driving, which might be faster than my level 2 charger.
Smart mode does automatic switching between Eco and Sport modes. It watches your driving habits, such as how hard you accelerate, and whether you "repetitively operate the steering wheel." If you do that a lot, it goes into Sport mode, at least for a short period of time. If you drive gently, it goes into Eco mode.
Snow mode is documented as an automatic selection that occurs when the temperature is low and wheel slippage is detected. It reduces acceleration responsiveness. My car's drive mode selector wheel has a Snow mode position at the SSE position. This is undocumented, and I don't know whether the automatic selection of snow mode can still happen.
Hybrid Mode
Hybrid mode determines how quickly the battery drains. You set the hybrid mode with a button on the console.
There are three hybrid modes: Electric, Hybrid, and Automatic.
Electric mode is the default, and it means that the motor will be preferred over the engine. It's the charge depleting mode - you'll use the motor until the battery is drained. However, the engine will still be used under certain conditions, some of which are rather unpredictable. If you accelerate hard enough, the engine will kick in. Additionally, the engine will come on to provide cabin heat, or to warm other components. The engine might even come on from time to time when driving gently in warm weather with a full charge. It has a mind of its own.
Hybrid mode "Hybrid" is charge sustaining mode - it preserves the current level of the battery. The engine is used almost exclusively. Still, the motor will be used from time to time, as regenerative braking can replenish it. It's more accurate to say that the Hybrid hybrid mode maintains the battery in a narrow range surrounding the current level. You might use this mode on the highway, so that you can then change to electric mode for city driving.
The third hybrid mode is Automatic. I suppose it's meant to automatically change between the other two hybrid modes, but based on what I don't know. In my experience this mode behaves pretty much like the Hybrid (charge sustaining) mode, but it will let the battery deplete to about 80%. I tend to use automatic mode on long trips, in the belief (or hope) that it will maximize MPG by using the battery from time to time, while depending on regenerative braking to recharge it from that use. I also use it to preserve battery power that I can use later for city driving.
Summary
In summary, drive mode and hybrid mode are independent settings. Drive mode affects the driving experience, primarily measured by acceleration responsiveness. Hybrid mode affects the degree of battery use. There's a bit of interaction between the modes, especially since selecting Sport drive mode prevents a selection of Hybrid mode.