A good seller selects good components, does not cheap out on decoupling capacitors, shows a schematic, and sometimes even a tutorial, and sometimes a forum to ask questions.
Bad quality causes problems when you don't expect it. For example a SD card socket that does not have good contacts, or a noisy board that stops working with another noisy board, a fake sensor that breaks at a certain temperature, a soil moisture sensor that lasts only a week, a rechargeable battery that is overloaded, and so on, the list is endless.
Maybe we should have a poll: what percentage of AliExpress/Ebay/Amazon cheap electronic modules is really really bad. My guess is 50%.
Start with real Arduino things.
Hmmm
I didn't know that Arduino has the same motor shield: https://store.arduino.cc/products/arduino-motor-shield-rev3
Or make a step forward with the MKR boards. Add a MKR Zero to this shield: https://store.arduino.cc/collections/shields/products/arduino-mkr-motor-carrier
Have a look at Adafruit, they make the best tutorials.
This is their well known motorshield: https://www.adafruit.com/product/1438
Sparkfun has this motor shield, simple and good: https://www.sparkfun.com/products/14451
Pololu is specialized in power and motor drivers: https://www.pololu.com/category/11/brushed-dc-motor-drivers
The most important thing is the stall current of your motor.
If you motor is 500mA average current, and the stall current is 10A, then you need a motor shield (or "driver" module) that can deal with 10A and you need a power supply that give 10A.
In the photos, the pins seems like good square solid pins. Do they look the same on your shields ? If I were you, I have a good look at the shield and if they look okay, then I would use them.
Do you have a multimeter ? Then you can measure the voltage at the analog pin and check why it changes with the motor shield.
Maybe you need a normal LCD module/shield anyway. This is a normal LCD shield: https://learn.adafruit.com/assets/36490.
There are probably cheap clones of that shield on Amazon. But if you have to throw away the cheap rubbish because it works only for a day or two, then you better aim higher and spend some money.
Sorry for the long post 