There's no such thing as "customer-led". That's not a common term, or when it's used it's used so generically as to mean pretty much everything.
"Product led" describes specifically what a "product manager" is hired to do -- make trade-offs primarily between engineering and sales (as well as take into consideration management priorities and general user satisfaction, but user satisfaction is only one priority out of many -- and often not the top one, either).
And if "sales-led" or "engineering-led" resulted in business success then product managers wouldn't exist, because they wouldn't be needed. But sales and engineering often have very conflicting priorities, and would result in drastically different products if left to their own devices.
There's no such thing as "customer-led". That's not a common term, or when it's used it's used so generically as to mean pretty much everything.
"Product led" describes specifically what a "product manager" is hired to do -- make trade-offs primarily between engineering and sales (as well as take into consideration management priorities and general user satisfaction, but user satisfaction is only one priority out of many -- and often not the top one, either).
And if "sales-led" or "engineering-led" resulted in business success then product managers wouldn't exist, because they wouldn't be needed. But sales and engineering often have very conflicting priorities, and would result in drastically different products if left to their own devices.
Hence, product-led.