This a new (GPM-formated) TRMM product. There is no equivalent in the old TRMM suite of products.
Version 08 is the current version of the data set. Older versions will no longer be available and have been superseded by Version 08.
The "CLIM" products differ from their "regular" counterparts (without the "CLIM" in the name) by the ancillary data they use. They are Climate-Reference products, which requires homogeneous ancillary data over the climate time series. Hence, the ECMWF-Interim (European Centre for Medium-Range Weather Forecasts, 2-3 months lag behind the regular production) reanalysis is used as ancillary data to derive surface and atmospheric conditions required by the GPROF algorithm for the "CLIM" output. The GPROF databases are also adjusted accordingly for these climate-referenced retrievals.
3GPROF products provide global gridded monthly/daily precipitation averages from multiple satellites that can be used for climate studies. The 3GPROF products are based on retrievals from high-quality microwave sensors, which are sensitive to liquid and ice-phase precipitation hydrometeors in the atmosphere.