The two star catalogues are the Flamsteed and the Henry Draper (HD) numbers. Flamsteed gave numbers beginning with `1' to stars in each constellation. The Flamsteed catalogue is small and doesn't contain the complete southern sky. In contrast to that, the HD catalogue doesn't distinguish between constellations, it covers the whole sky, and also contains faint stars. However the HD names are harder to read.
For example Rigel, \beta Ori, can be identified in PP3 with either
ORI 19
where `ORI' is Rigel's constellation (Orion) and `19' the
Flamsteed number; or with
HD 34085
where `34085' is Rigel's Henry Draper catalogue number. Both are
totally equivalent. The free program
Celestia is very useful
for finding Flamsteed or HD numbers.