They are not data types. They are integer constants that have one of the bits set.
1 2 3 4 5 6 7 8
#define paFloat32 ((PaSampleFormat) 0x00000001) // first bit set
#define paInt32 ((PaSampleFormat) 0x00000002) // second bit set
#define paInt24 ((PaSampleFormat) 0x00000004) // third bit set
#define paInt16 ((PaSampleFormat) 0x00000008) // fourth bit set
#define paInt8 ((PaSampleFormat) 0x00000010) // fifth bit set
#define paUInt8 ((PaSampleFormat) 0x00000020) // sixth bit set
#define paCustomFormat ((PaSampleFormat) 0x00010000) // seventeenth bit set
#define paNonInterleaved ((PaSampleFormat) 0x80000000) // thirty-second bit set
They are probably meant to be used with bit masks to allow multiple of them in the same value.
PaSampleFormat frmt = paInt24 | paNonInterleaved; // non-interleaved 24 bit integer format