The Bristow one is an oil exploration contract which has to provide its own SAR cover for transporting pax to and from the rigs; they operate out of Stanley airport.
The other is an Falklands-wide passenger and freight transport for the FI government which has been provided by Brintel (part of BIH) for many years; they operate out of Mount Pleasant Airfield.
The SAR contract is new because the RAF Sea Kings that have provided this function (primarily for the recovery of fast jet crews) are going out of service shortly and, along with UK SAR, is being civilianised.
Sensibly, the FISHSAR (Falkland Islands Support Helicopter and SAR) contract combines the two elements and will continue to operate out of Mount Pleasant.
Does that answer your question?