The SEALS as we know them today were an important part of the Allied amphibious landings in Word War Two. They are a very small force that has been around for a long time.
Underwater men have been important to the military for a long time. ""In 1942, the Army and Navy jointly established the Amphibious Scout and Raider School at Fort Pierce, Florida. Here Lieutenant Commander Phil H. Bucklew, the “Father of Naval Special Warfare”, helped organize and train what became the Navy’s ‘first group’ to specialize in amphibious raids and tactics.""
There were only UDT in WWII, but no SEALs, who were created in 1962 and we had SEALs and UDT simultaneously for 20 years, until 1982 when UDT was ended and most UDT went into the SEALs (after getting additional training to make the SEALs.
While the SEALs trace their lineage to UDT, I think it would be misleading and confusing to now start calling the WWII and pre-1960s UDT, "SEALs" although now UDT and SEALs have been melded into one, it would be similar to calling WWII OSS Army Special Forces, or "Green Berets".
""Pressure to further implement human intelligence gathering prior to landings heightened after Marine Corps landing craft were damaged by coral reefs during the Battle of Tarawa in November 1943. Aerial reconnaissance incorrectly showed the reefs were submerged deep enough to allow the landing craft to float over. Marines were forced to abandon their craft in chest deep water a thousand yards from shore, helping Japanese gunners inflict heavy U.S. casualties. After that experience, Admiral Kelley Turner, Commander of the 5th Amphibious Force, directed that 30 officers and 150 enlisted men be moved to Waimanalo ATB (on the “big island” of Hawaii) to form the nucleus of a reconnaissance and demolition training program. It is here that the UDTs of the Pacific were born.”""