The replies are great. I do have to disagree however. Unless specifically stated, they are very different. Internal processing does not determine recording bit depth, just how it is processed once the bit depth has already been determined, as noted by the pictures above.
https://www.sounddevices.com/how-is-a-32-bit-float-file-recorded/
32-Bit Float WAV Files
The WAV file is a universal container for audio data, capable of storing material in a variety of bit depths, including 24-bit fixed point, 32-bit fixed point, and 32-bit floating point. In order to maintain the benefits of 32-bit floating point audio, audio data must be stored as 32-bit floating point. The audio application which is receiving the 32-bit float WAV files needs to support this format. While many audio applications do support 32-bit float, support is not yet universal.
How Is 32-Bit Float Different From 32-Bit Integer?
32-bit float signals should not be confused with 32-bit fixed point. A 32-bit fixed point signal can accommodate considerable dynamic range, roughly 192 dB. While 32-bit integer offers a much larger dynamic range than 24-bit audio’s theoretical 144 dB, it pales when compared to the 1500 dB available to 32-bit float signals. If, for instance, processing adds 90 dB of gain to the 142 dB of dynamic range coming in, then 232 dB would be needed to capture this signal with no loss in headroom or noise. 32-bit float can do this, and 32-bit integer cannot.