In the US the first test administered is usually ishihara, if you fail this then there are a large number of alternative accepted tests approx 15 in total a pass in any one of these is good enough for life. You will be given a letter from the FAA saying that you meet the standard so that you can show it to subsequent medical examiners who may not have the test that you passed.
If you fail all the accepted tests the there is one final test that you can do, it is the signal light test. What happens is that you get your medical from the FAA with the restriction prohibiting night flight and flight by color signal control, then you make an appointment with the local FAA office and they take you out onto an airfield with an FAA control tower. The control tower flashes light signals at you and you have to name them to the inspector standing next to you. The test is done at 1000ft distance and repeated at 1500ft, the order of the colors is random. If you pass you get the same letter as above, good for life.
The signal light test can be passed by most people. It has been used by the FAA since the FAA's inception in 1958 and previously used by the FAA's predecessor since flying started to be regulated. Thousands of pilots have been passed by this test alone and their historical safety record is 100% (never has a pilot who can pass this test been involved in an accident or incident where he confused safety critical colors)
This signal light test is also used in Australia.