From AMS Glossary
The amount of precipitation of any type (including the liquid equivalent of frozen hydrometeors); usually taken as that amount measured by means of a rain gauge (thus a small, varying amount of direct condensation is included).
A more accurate term would be precipitation or precipitation amount. However, the broad use of "rainfall" is firmly established in meteorology, especially in hydrologic and climatological literature. Its best utilization would confine it to liquid precipitation, and so would provide a distinction between precipitation immediately accessible to soil and streams and that delayed in storage as snow or ice on the earth's surface.