Difference using a wireless adapter?

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What is the difference between using your built in wireless adapter in your laptop and using a external wireless adapter to capture packets?

One difference would be in the antenna - the built-in adapter probably has a built-in antenna somewhere in the laptop body, while an external adapter either has its own antenna in the adapter or has an antenna that plugs into the adapter. The different antenna types might make a difference in the reception quality for a monitor-mode capture.

The only difference in the software stack would be the driver, if the built-in adapter and the external adapter use different drivers, but that's not a matter of built-in vs. external, they're adapter A vs. adapter B, even if they're both external - some adapters might be better at monitor-mode capture than others.

Nothing above that in the networking stack, all the way up to the application doing the capture, would differ between built-in and external.

Another difference would be that, if you're using your built-in adapter for networking, using it for monitor-mode capture might disconnect you from your network, while using an external adapter wouldn't.