On Windows 7 and Windows 10 if a computer is connected to the same network by both Wi-Fi and gigabit wired, Windows will prefer and use the wired connection by assigning a better (lower) metric to that network adapter - use the "route print" command to confirm this.
The priorities can be manually re-ordered and some people do this intentionally or inadvertently when trying to solve some other problem, such as if they want to override a wired connection while tethered to their smartphone.
The situation might be different if the wireless channel width is configured so wide and the laptop and AP have enough spatial streams that the link can report a data rate faster than 1Gbps but this is an edge case.
On the IP conflict thing, if DHCP, one or both PCs will release the IP and restart DHCP discovery.
Checking for IP already in use on the network (ARP) before making an offer is part of the protocol, even if the DHCP server doesn't think it has already leased this IP.
Even if manually assigned IPs and conflicting, on the affected computers Windows would normally popup an alert as well as a flag on the network icon in system tray (in older versions at least).
And if there was an IP address conflict they would still have problems copying files to and from the NAS, because the affected computers would be constantly trying to assert "I have the L2 Ethernet address for that IP" (ARP), even if the second computer was not the source or destination of the file copy.
TL:DR (Wi-Fi?) you don't have to guess because you can run the command to check
prlzx on iDNET: FTTC (VDSL) at ~40Mbps / 10Mbps
with IP4/6 (no v6? - not true Internet)
Edited by prlzx (Sun 21-Jun-20 12:12:40)