"Ping" is such a misunderstood term.
It is the total time it takes for a round trip between your system and wherever.
The LAN device on your system only affects the "ping" between you and your router.
Ping to anywhere...the first hop is to your router.
This should be <1ms. That is the only thing your LAN adapter and driver can influence.
After your modem/router...you have little influence over what happens.
In broad terms, the farther away you are from the target server...the higher the ping.
Dozens or hundreds of routers and servers in between.
Please show us some links where someone says there is a difference between intel and realtek.
So that we may debunk them properly.