The allocation unit size is a term of the file system (operating system software) , the sector size is a term of the underlying hardware.
File systems do not necessarily use single sectors to manage drive space.
Sometimes they combine single physical sectors into a logical administration unit. The size of such a bunch of sectors is called "allocation unit size".
When formating a partition you typically have the choice to set the "allocation unit size" (cluster size in Microsoft operating systems).
A common combination in the NTFS (Microsoft file system, used in Windows operating systems) is to combine 8 sectors with a size of 512 byte into a so-called "cluster". Cluster seems to be the Microsoft equivalent of the more generalized term "allocation unit size". This cluster size of 4096 byte is the minimum increment/decrement when occupying/releasing storage space.