Beta using only price returns?

It is my understanding that one can use both excess returns and price returns to compute a beta coefficient. In the former way, beta would be interpreted in the standard way (a 1 unit change in market excess returns is associated with a beta unit change in share excess returns). In the latter way, you have the same interpretation but only considering the actual returns of the market and the shares. In this sense, using both excess returns and price returns are both valid ways to compute beta. Co