A full scan is one in which as much detail as possible is collected about the target. This can include scanning all ports, interrogating services for versions, footprinting the operating system, etc. This can be used with either TCP or UDP, though UDP will take considerably longer as the scanner must wait to time out if no response is received on that port. Full scans produce the most results, but are also the "noisiest" and the most likely to be detected. Common ways to evade detection include randomizing the IP addresses and ports, and slowing the scan down. Here are some Nmap full scan examples:
nmap -p- 192.168.1.0/24
nmap -p1-65535 www.technoherder.com
nmap -sU -p1-65535 192.168.1.50
Note: Some also use the term "full scan" to refer to a TCP connect scan nmap -sT <target>, in which the three-way handshake is completed.