The names of the lighting systems get longer as the lights get more complicated. I realize now that the reason I didn't know the differences among these types is that they are very similar. MALSR and SSALR consist of a 1000' centre row of sequenced flashing lights leading in to a wider and 1400' long array of non-flashing white bars. There's a good diagram of the MALSR layout here, on a manufacturer's website.
MALSR apparently stands for "Medium Intensity Approach Lighting System with Runway Alignment Indicator Lights". I guess they realized that MIALSRAIL wasn't credible as a cool aviation abbrevitation. There's also the "Simplified Short Approach Lighting System with Runway Alignment Indicator Lights" or SSALR, which has a pretty much identical layout, but is apparently more intense. Which is odd, because all of these have adjustible intensities.
MALSF, Medium Intensity Approach Light System with Sequenced Flashing Lights, sounds as if it describes MALSR, but has a slightly different layout, in that the initial string of sequenced flashing lights alternate with steady bars. It's also shorter, coving only 1400' all together, so basically the sequenced flashing lights are incorporated into the 1400' of wider bars, instead of leading up to it. I suppose these can be used in places where the MALSR or SSALR can't be, because of terrain or space considerations. I have a link to a manufacturer's diagram of the MALSF, but it's a pdf.
One more sort of lighting to contend with, before I go back to amusing stories about parts falling off my airplane while I am flying it.