power, multiplication, record, counter for vehicles
乘 centers on the idea of riding or mounting something, which extends to the power of a vehicle, the multiplication of records, and counting vehicles. The core is about being carried or elevated by something.
乘 is the traditional form of 乗. It originally depicted a person climbing onto a tree or vehicle, with the lower part suggesting a base or support. The modern simplified form 乗 is more common in Japanese.
The top part looks like a person (ノ and 十) climbing onto a vehicle or base (ハ, 匕, 爿). Imagine someone stepping up to ride, which gives the sense of power, multiplication, and counting vehicles.
For ジョウ, picture a person named Joe climbing onto a big vehicle: Joe -> ジョウ, and Joe rides the vehicle, showing its power.