Below we contrast the different weapons available to the UDT/SEAL teams during the three major conflicts they have particpated in. Note that at first UDT teams had no transport gear of their own, relying upon the U.S. Navy to move them to the beaches. In fact, they were swimming mostly fully clothes with deck shoes to keep their feet from getting cut by coral.
Later it occurred to the commanders that if the men were to be swimming, it would increase their strength and longevity in the water if swim trunks were worn. Finally it became clear that Navy divers sould have fins. At one point all the fins available in the U.S. were found on the feet of UDT team members.
The aqualung was used primarily for underwater repair, and was not used for demolition or other clearing work until the later years of World War II.
Today's SEALs use whatever land or marine based gear is necessary, and the elite of the elite, SEAL team 6 also has a full arsenal of counter-terrorist gear including "flash bang" concussion grenades, fiber optic camera probes, listening devices, sharpsthooter rifles, superb night vision equipment, and much much more.
Another key development is that Navy SEALs have much of their own transportation equipment on hand, from small rubber boats, through Zodiaks and small assault boats much like the Riverine craft in Vietnam. It is not clear in the new operations of USSOCOM, whether SEALs now have their own helicopters....however it is doubtful, they probably still have to rely upon the USSOCOM air operations units (Air Force Air Commandos or Army's 160th Special Operations Aviaition Regiment).