It should be said that Sollya doesn't _really_ use floats. It restricts its coefficients to rationals that are (mostly) representable by floats, but the minimax is still run in full precision. Which means you can often beat it by brute force or similar.
Yes, that is a good clarification - it uses wider precision internally, but it takes floating point restrictions and operations into account. If you otherwise used Remez, you would have to just quantize the coefficients blindly and then tweak (probably manually) if something was off.
Shamelessly plugging, you can sort of see the old-school process here (using integers and mixed-precision fixed point is harder with Sollya): https://specbranch.com/posts/faster-div8/
The coefficients and constants in both cases are substantially higher than what you get from Remez, to allow for truncation. When you have quantized operands, they are quite a bit higher. The same goes for approximations generated by Sollya - the optimal coefficients are relatively far from what Remez would tell you to do because of the error you get from rounding.
