How to distinguish between appreciation and inflation?

Inflation is a general up trend in price when value remains unchanged. Hence "the same thing" suddenly costs more.

Appreciation is a bona fide increase in value. This tends to also increase the price that the market will pay.

Thus put, the difference is clear: value_final - value_initial = appreciation and appreciation + inflation = price_final - price_initial The problem of course is that it is very hard to accurately determine value. There are ways - but ultimately, almost all measures of value are more or less contaminated by inflation.

You can go the other way and simply measure the inflation, and then work back to get appreciation. This is somewhat circular in that inflation is defined in relation to value. This is where things like CPI come in - the premise is that the benchmark is either inherently unlikely to appreciate much, or the appreciation happens to be very predictable. Of course, it is debatable whether you can assert that there is any asset which does not appreciate or depreciate over a given time. But if you trust the government's CPI (or any other's source's), then you can use it to infer appreciation, and the appreciation will be accurate to the extent that the CPI is accurate.

So let's say:

• CPI was 2% over last 10 years
• You bought a house 10 years ago for 200k
• The house is now 300k

You have a price difference of 100k or 50%. The inflation alone would have resulted in 244k, so we can consider the 56k to be appreciation.

I know I could look at conventional inflation measures (like CPI) and compare against the performance of the asset in question, but one could argue certain baskets of 'things' haven't been impacted by inflation at the same rate because of lower/higher money velocity

Your basic approach is correct. You take measured inflation and subtract it from your gains. The problem is measuring inflation. The problem you have spotted is that measuring some basked of things is not necessarily measuring "true inflation", but this does not have anything to do with money velocity. The problem is based on a much simpler issue: inflation for different things is different.

Let's say the price for gas is decreasing but the price for TVs is increasing. How do you weigh this? You can build some basket, average things out and postulate this as the official inflation rate. But this is just an approximation and it will inevitable be different from the inflation everybody feels. Even worse, it may miss entire categories, e.g. in some countries only rent (=pretty sticky prices) is counted towards inflation but not self-owned homes (which are a lot more volatile in price). How do you properly account for categories where prices are falling fast like consumer electronics? After all, something comparable to the flagship phone of today will be available for like 200$ in the pretty near future. Additionally there is the problem of actually measuring prices. How do you treat items that are currently on sale? What is the price of a flight with airlines changing prices all the time? (Bonus question: how do you measure the price of a service if that is unavailable during lockdown times?) All of these issues make CPI a not so suited measure for inflation.

A probably better way to judge inflation over long time periods is to compare your asset to incomes. After all, no matter what we count or not, if things get more expensive overall, people will demand higher wages. Over the long run, this should roughly be on par with the actual inflation