Each organization overlaps with the others, slightly, and each serves a unique purpose.
United Hatzalah is the main body of “Hatzalah” as we in the US and UK know it. They unified most local branches of Haztalah into a single body. Their primary goal is to get onto the scene as quickly and possible and provide initial lifesaving support in the field. In many/most situations, they work together with Magen David Adom (MADA) for emergency transportation, but they also have transportation ambulances in some areas. This is why United Hatzalah has a lot more bikes and ambucycles, with fewer ambulances. United Hatzalah consults with the chareidi gedolim on all issues, has halacha courses mandated for all volunteers and includes volunteers from all walks of Israeli life.
There are local branches of Hatzalah that for different reasons prefer to remain separate from the national body under HaTsadik Eli Beer. No tainas on them, and this doesn’t reflect poorly on United Hatzalah either.
Magen David Adom (MADA) primarily serves as emergency medical transportation team with emergency response capabilities. MADA is run as a semi-government-run, semi-volunteer organization. They also now have some ambucycles for emergency response.
In the past there were politics. Nowadays, nearly all of them collaborate on most calls. When we called Hatzalah, they arrived within 2 minutes. They call in MADA, who came 8-10 minutes later for the transport. They are all worthy tsedakas.