Does a PS 4 have different IP addresses or different MAC addresses via WLAN or LAN?
MAC is one and the same.
However, IP addresses depend on the network.
MAC address is the "serial number" of WLAN, LAN and, for example, LTE chipsets
You get either a v4 or a v6 or even both per device, depending on the setting of your router, among other things.
Yes and yes. An IP device gets its IP address from a DHCP server. The DHCP server assigns the IP addresses to be assigned to different MAC addresses. The MAC address is the "hardware address" - and since LAN and WLAN are two different chips, they are also two different MAC addresses.
The DHCP server reserves an IP address Y for a MAC address X for a certain period of time. If the MAC address X reports to the DHCP server again during this period, it is assigned the same IP address Y again.
If X is the LAN chip in this example, you will get a different IP address via WLAN, since the one already reserved applies to the LAN chip.
A PS 4 has different IP addresses via WLAN or LAN
As a rule, the LAN and WLAN devices have the same IP to the outside world. Unless you have 2 internet connections, which is rather unlikely.
Internally (in the home network) the devices naturally have different IP addresses
or different MAC addresses?
The Mac address depends on the network adapter, meaning that a PS4 has a different MAC address on its LAN port than on its WLAN.
Is the serial number
No. A serial number is semantically something completely different. Serial numbers are also continuous, while MAC addresses have manufacturer-specific parts, but are still generated randomly.
This is wrong. Each network adapter / network card has a different MAC address. The PS4 has 2 of them. Once for LAN, once for WLAN.
Then explain to him what a MAC address is as simply as possible
Can you be connected to the PS4 via LAN and WLAN at the same time?
Yes you can. Whereby the cable connection would be preferred and the WLAN connection would probably just chill out. So it's pointless to have both up and running somewhere.