Wikipedia says the British lost 24 helicopters while the Argentinians lost 25. Did the British losses at sea make up some of their lost Helicopters or were the destroyed Helicopters involved in interdiction/resupply/casualty evacuation during the ground battles in the East Falkland.
Also were the aircraft destroyed by other aircraft or MANPADs or other ground based anti aircraft weapons?
Nearly half of the British helicopter losses took place on the 25th May 1982. Most of these losses took place aboard SS Atlantic Conveyor. This was a container vessel, which had taken aboard 11 helicopters for transit to the Falklands. She was sunk by an Exocet missile on the 25th May 1982, with the loss of all but one helicopter aboard. On the same day, HMS Coventry was sunk with her Wessex helicopter still in her hangar. The majority of the rest of the British losses were accidents. Two crashed in a snow storm on the Fortuna Glacier in South Georgia, while trying to insert SAS troops to recapture the island. Four Sea Kings were lost in several accidents at sea, while an Army Scout crashed into a lake. These were the result of mechanical failures, although one may have been a bird strike. One Gazelle was shot down by HMS Cardiff by mistake. Another Sea King was blown up by its crew after landing in Chile while trying to deploy an SAS recon team to the Argentinian airbase at Rio Grande. Of the remaining losses, one Scout was lost to a Pucara aircraft. Two Gazelles were lost to small arms fire near San Carlos. A Lynx was lost along with HMS Ardent on the 21st. The final aircraft was lost when HMS Glamorgan's hangar was damaged by an Exocet. Discounting those lost at sea, the majority of the losses occurred on transport and reconnaissance flights.
Argentine helicopter losses began on the 3rd of April, with a Puma helicopter ferrying troops onto South Georgia being shot down by Royal Marines with small arms fire. On the 2nd May, a Lynx from ARA Santissima Trinidad was lost in an accident, while ARA General Belgrano's Alouette went down with the ship when she was torpedoed. On the 9th May, a Puma was shot down by HMS Coventry with a Sea Dart missile. Two Pumas were destroyed on the ground by RAF Harriers on the 21st. On the 23rd, two more Pumas and an A-109 were destroyed by RN Harriers. These helicopters had been spotted in the air, but either landed or crashed before the Harriers could engage them. The two that landed were strafed and destroyed. A final Puma was lost in mysterious circumstances near Mount Kent on the 30th, and may have been shot down by friendly fire. The remaining losses represent those captured by the British when Argentine forces on the Falklands surrendered. The Argentinians mostly used their helicopters to supply their outlying bases, and the losses on the 9th, 23rd and 30th occurred during such resupply operations
Naval-history.net's Falklands page has basic information on the losses, but for more detail, I used Max Hastings' and Simon Jenkins' Battle for the Falklands.
Poeple will add more and I haven't got the time to flesh out a lengthier response, but in particular for losses on the British side - the sinking of the Atlantic Conveyer (https://en.wikipedia.org/wiki/SS_Atlantic_Conveyor) resulted in the loss of ten helicopters, including all but one of the expeditionary force's Chinooks. This resulted in troops needing to march long distances to carry out the operation. ('Yomping').