there's also a couple of sources and differences: the main one commonly quoted is the ABS source, derived from the census taken every 5 years, and with specific practices implemented to try to accurately enumerate homeless populations. thankfully there doesn't seem to be enough variance for the relative infrequency to be an issue, but the other quirk is that census is done in winter, and contrary to some popular impressions, homeless populations can be highly mobile and show seasonal effects.

Another source include homeless service provisions, but last time I looked at those they didn't always tend to be on a individual natural person basis.

lastly, homeless service provision, with a few caveats, is one of the only things that might locally and empirically show behaviours of what economists call a "giffen good". And, somewhat paradoxically, provision of homeless services can, to a point, increase the percieved systemic demand for homeless services. increased supply can also create more (real and percieved) demand. the relationship these complexities have with trying to measure homelessness is tricky to say the least...