Different names means they are different. Take a look.

While walking through our gardens, the F1 asked a good botanical question.  Is that just a pale squill or is it something different?  The answer is actually it was just a pale squill, but in another part of the gardens there is another species that looks superficially like a pale squill.  Here they are together.  The pale squill looks just like regular squill except it is a  nearly white pale blue. What you see here is Scilla siberica (left) and Pushkinia scilloides (right). The flower sizes are similar especially when newly opened, and the coloring along the midvein of the showy perianth (petals) parts is darker.
The squill perianth opens more widely.  The Pushkinia stays more bell shaped.  Flipping them over shows a lot more differences.  The squill has longer stamen filaments and blue anthers, and usually only 1 or 2 flowers per stalk.  The Pushkinia has shorter, flattened filaments fused into a column with yellow anthers on the inner surface surrounding a smaller pistil, and usually more than 2 flowers per stalk.  Now to make matters slightly more complicated, your lawn might also have (TPP doesn't, but his previous lawn did.) Chionodoxa, glory of the snow, concurrently flowering as well.  Its flowers are also blue, but tend to be slightly bigger, to face more upwards, and to have  lighter-colored centers.  Both can naturalize and spread across your lawn.