Raw Home Price Index is the same as the Inflation-Adjusted Home Price Index, except that it includes the effects of general inflation (purchasing power). In other words, it's the "nominal" cumulative price path — what prices actually did in dollar terms, before inflation is stripped out.
Use the inflation-adjusted version when you want to isolate true Supply & Demand; use the raw version when you want the nominal, headline price movement. Chart either in Custom Charts PRO and overlay them to see how much of a market's gain was real vs. inflation.