Some of the types:
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MALSR: Medium-intensity Approach Lighting System with Runway Alignment Indicator Lights
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MALSF: Medium-intensity Approach Lighting System with Sequenced Flashing lights
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SALS: Short Approach Lighting System
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SSALS: Simplified Short Approach Lighting System
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SSALR: Simplified Short Approach Lighting System with Runway Alignment Indicator Lights
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SSALF: Simplified Short Approach Lighting System with Sequenced Flashing Lights
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ODALS: Omnidirectional Approach Lighting System
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ALSF-1: Approach Lighting System with Sequenced Flashing Lights configuration 1
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ALSF-2: Approach Lighting System with Sequenced Flashing Lights configuration 2
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CALVERT I/ICAO-1 HIALS: ICAO-compliant configuration 1 High Intensity Approach Lighting System
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CALVERT II/ICAO-2 HIALS: ICAO-compliant configuration 2 High Intensity Approach Lighting System
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LDIN: Lead-in lighting
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REIL: Runway End Identification Lights
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RAIL: Runway Alignment Indicator Lights
Source, Wikipedia.
(Also @bookers4eva the REIL lights are wrongly marked on that pic)