The answer takes you back to general chemistry.
The Hanna Phosphorus ULR checker (HI736) measures phosphorus, in other words, the stand-alone element P. This checker measures in units of parts per billion (ppb), in other words one billionth of a gram of phosphorus for every gram of water.
The Hanna Low-Range checker (HI713) measures phosphate. The phosphate compound is one P with four O atoms. This checker measures in units of parts per million (ppm). 1 ppm is one thousand times higher concentration than 1 ppb. One mole of phosphate weighs more than one mole of phosphorus (moles, from general chemistry), in fact it weighs 3.13 times as much, so you cannot go directly from ppb of phosphorus to ppm of phosphate. But you can convert from ppb of phosphorus to ppm of phosphate by multiplying by 3.13 and dividing by 1000 (or just multiplying by 0.00313).
Most of the discussion of nutrients in fish tanks talks about phosphate in ppm, so that's the compound and number you want to use or to get you. The Low-Range phosphate checker gives you phosphate directly, so that is useful. But its accuracy is 0.04 ppm, meaning it is harder to know if the difference between 0.01 or 0.02 (or 0.01 vs 0.05) is real or just variability among measurements. The ULR phosphorus checker gives you values as phosphorus (so you need to do that multiplying) but it has an accuracy of 5 ppb. When you multiply that by 0.00313 to get phosphate, you see that you can better trust the difference between 0.01 vs 0.02.
It looks like there is now a Hanna Ultra Low Range phosphate checker, HI774 that combines the better resolution of the ULR phosphorus checker with the gives-you-phosphate of the Low-Range checker. It looks like Hanna gives is slightly less accuracy than the ULR phosphorus checker but better than the Low-Range phosphate checker.
But thankfully, my b-n-l is a chemical engineer and is only a phone call away.
