Let me share here the answer Stephen Coles gave me on Quora :
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The reason for the two versions is that Charter was initially designed by Matthew Carter for Bitstream and then later licensed to ITC. I am not aware of any discernible letterform differences, but there are some differences in price, character sets, metrics (spacing, kerning, bounding box size, etc), and probably hinting (optimization for Windows screen displays). There are also Standard and Pro versions from each foundry.
To make the decision simpler, you probably want to narrow your choices down to Pro versions so you have most of what you need for language support (beyond Western Europe) and typographic features (small caps, oldstyle figures, etc.)
So your choices are: ITC Charter Pro and Charter BT Pro.
ITC Charter claims more glyphs at 695 versus 613, but it’s not clear at a glance what those extra glyphs are, since both fonts have the same language support and typographic features. (They are probably some historical forms and other rarely used extras.)
The prices between the two versions are nearly the same, both for single fonts and family packages, so it comes down to other two other main factors: metrics and hinting. I did some quick testing and did find differences in the kerning, but nothing major. So the final distinguisher is hinting, and that I cannot judge without a system running Windows. Hopefully one or both versions have been manually hinted. You’ll have to test them to be sure. (Ask MyFonts for browser screenshots! They used to supply them but they disappeared sometime last year.)
There is also a third foundry, ParaType, that offers a Charter with Cyrillic character support. So if you need your text to be read by the many millions in Russian-speaking regions, go for that one.