What do the Linux interface names mean?
My current assumption is that when we are connected to the Internet via LAN cable it's eth0 or eth1 and when we are connected with internet via WiFi it's wlan0.
Your assumption is correct.
The names however can be set/chosen by the user or the operating system that you are using.
eth1 is used because it's more intuitive than choosing an arbitrary name because "LAN cable" connection, like you said is Ethernet (hence the
eth0, eth1). Similarly when you connect to WiFi, it's "WirelessLAN" (hence the
eth0 is the first ethernet interface, any additional ethernet interfaces would be named eth1, eth2, etc.
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