Logic library (for example, it is synopsys liberty file or synopsys library) contains timing, power, noise, logic (sometimes) info about cells. If the cell is complicated enough (like sram), this library may not contains logic (behavioral) description.
Physical library (for example Synopsys milkyway database) contains real layout(topology) of the cells, and some simplified (abstract or phantom or FRAM) view of this topology.
Logical library is the technology library that you use to map the design for a specific technology node from the foundry(standard cell and memories / macros /pads)
For the same logical cell you will have a physical library (LEF) which will carry the cell footprint of each logical libcell in the library again for both memories / standard cell macros and pads. These LEF files are more important from a implementation point of view.
Now each of the logical libcell will have a functional definition and the physical library or LEF will only have the footprint of that libcell making it the physical library
Many cells which do not have functional purposes only contain physical libraries for example FILLER cells ENDCAP etc