Is it the same as DHCP exhaustion? Can LANs be vulnerable to such attacks or it's against WiFi only?
Well Wifi or 802.11 is a protocol used at layers 1 and 2. DHCP works on layer 7 and uses a broadcast message to the whole network to which any DHCP server will/may reply to. So it's not only related to wifi it's, as Rory mentioned, applicable to any network using DHCP.
It's indeed the same as DHCP exhaustion. You as an attacker, will be sending tons of DHCP requests with spoofed MAC addresses to the DHCP server as to deplete the pool available IP addresses.
As @lucas explained how it works. The prevention from DHCP starvation attack can be achieved by using port security means bind the port with maximum number of allowed mac address. Since DHCP starvation works when multiple request send to the DHCP server, so this solution will assure that max number of arp requests. It can also prevent by using dhcp snooping means verify the mac address in dhcp request frame.