Actually there is a fifth connection - to battery negative. On yours this is via the bikes chassis. This is 'made' by one or more of the mounting screws and or the metal to metal contact between the rec/reg case and the frame. On some bikes there is a separate (usually black) wire to perform this connection.
But yes - most bike alternators have 3 wires .. and there is no electrical circuit difference between them so they can be connected anyway around. No point in having different colours on them. One failure mode is where the flexiable wire is slodered onto the stators less flexiable single core wire .. usually hidden inside some fiber tubing .. it fails by braking off - making an open circuit. If you can get to it you might make a temporary repair by soldering it back to gether and caoting it with araldite...
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Regards Frank Warner
motorcycles BMW R80 G/S 1981, BMW K11LT 1993, BMW K75 G/S
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