Quoting the Pysam Github repo description:
Pysam is a Python module for reading and manipulating SAM/BAM/VCF/BCF files. It's a lightweight wrapper of the htslib C-API, the same one that powers samtools, bcftools, and tabix.
I do not know which pybam you are referring to, you'd need to provide a link. It is probably any other project aiming to write software for NGS data manipulation in python.
OP is probably referring to this: https://github.com/JohnLonginotto/pybam
Author of that software claims it is probably faster than pysam, which is a bold claim to make, given their tool doesn't seem to use C++ or htslib.
EDIT: That software is abandonware made by someone with a bit of a holier-than-thou stance: https://github.com/JohnLonginotto/pybam/issues/7#issuecomment-427638328
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