The flippant answer is “…because they look alike”, and they can be very alike.

Two species of Yellowlegs, traced from photographs. Can you tell which is which? Original pencil drawing copyright David Sibley.
Most of what you read about yellowlegs will tell you to look at bill length to distinguish the species. The bill of Greater Yellowlegs is actually longer (50 mm or more, compared to Lesser’s 40 mm or less) but birders deal with impressions of size, not absolute measurements, so we rely more on the fact that Greater’s bill is relatively longer (compared to the head).
This is very useful, and with a little practice virtually all yellowlegs can be identified correctly by bill proportions. An important point to understand, however, is that bill length is simply a “handle” or starting point that we grab onto as we take in the overall impression of size and shape. As we become more familiar with all aspects of the species, we can rely on body shape, movements, facial expression, leg length, and so on. These are more subtle, ephemeral, or subjective things, hard to put into words, but once we gain that level of familiarity these other clues supplement our judgment of bill length. We might still say we are identifying the species by bill length, but it’s really a combination of many subtle hints, and if we encounter a yellowlegs that doesn’t trigger a strong match on bill length, we subconsciously shift to rely more on other clues.
The truth is that there are yellowlegs with ambiguous bill lengths.

Here is a long-billed Greater Yellowlegs above a typical Lesser, shown at their true size as if they were standing together. These are easy to identify.

Here are the same two birds, Greater above, with the size of the heads matched. Obviously the bill of the Greater is still relatively longer, and these "classic" individuals are easily identified by relative bill length.

Here are five yellowlegs, all traced from photographs, showing variation in bill length. The upper three are Greater, the bottom two are Lesser. There seems to be more variation in Greater, with some short-billed Greaters causing real ID problems. Still, combined with the smaller size of the Lessers, bill length is a strong clue.

This is the same image seen at the start of this post. It shows the shortest-billed Greater (upper) and a long-billed Lesser (lower), with head sizes matched to emphasize relative bill length. In this case the relative bill length is essentially identical.
The point of this discussion is not to discourage you from using bill length as a field mark to identify yellowlegs. Most yellowlegs can be identified that way, but it’s always good to use some other field marks to confirm your impressions of bill length. Don’t be surprised to encounter a yellowlegs that is difficult to pin down on bill length alone. You can help prepare yourself for those cases by learning some of the other field marks, including voice, that can be used along with bill length to identify the species.
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I primarily rely on bill length to identify Yellowlegs but you’re right, it’s always good to consider other fields to better identify them.
What about the slightly upturned bill in the GYL? That seems to be a pretty good mark.