Hi,
There are no differences between the “adafruits PCA9685” and NXPs PCA9685, in fact, the PCA9685 used in the adafruit’s board is from NXP. So, using the hardware from adafruit (PCA9685 board + Arduino Uno (or raspberry Pi)) and following the description of the page you sent, it should work fine.
Take in mind the note mentioned on the page when using Rasiberry Pi:
“Don't try to power your servos from the RasPi or Linux board's 5V power, you can easily cause a power supply brown-out and mess up your Pi! Use a separate 5v 2A or 4A adapter”.