Can someone explain the difference between Microsoft's MS-DOS and IBM's DOS? For example, does MS-DOS 3.3 and IBM DOS 3.3 have the exact same features?

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They're the same thing (only different) We've heard that a million monkeys at a million keyboards could produce the complete works of Shakespeare; now, thanks to the Internet, we know that is not true

Beginning with version 6, msdos and pc-dos are different things. The bits that were in DOS 4 (ie dosshell, edlin, etc) are preserved in DOS 6, but there are a whole lot of different utilities etc. msdos has a swag of defanged Norton stuff, while pc-dos tended to have full versions of older "Central Point" software. That is, for example, if the current version of the product were v7, then MS-DOS would have v7-lite, while PC-DOS would have v6-full. They used different editors (qbasic v 1.1, against e.exe v3.12), etc. Beginning with v7, rexx was integrated into pc-dos. The versions are then: msdos 6.xx 6.00, 6.20, 6.21, 6.22 ibmdos 6.xx 6.10 pcdos 6.xx 6.10, 6.30 pcdos 7.xx 7.00, 2000 = 7.00B, ibmdos and pcdos call themselves by these names. The dream you dream alone is only a dream, The dream we dream together is reality.