In the beginning, there was Unix, which was a product developed by Bell Labs (a subsidiary of AT&T). A lot of groups customized their copy and added their own programs, and shared their improvements with others (for pay or for free).
One such group was the University of California, Berkley (UCB). They shared the Berkeley Software Distribution (BSD) under a very liberal license (known today as the original BSD license). Originally, this was a set of additions to the basic Unix. Eventually, they rewrote the complete operating system, so that it could be used without getting a license from AT&T.
Apart from BSD, the main suppliers of Unix operating systems were computer vendors who sold the operating system with the computer. Some kept basing their operating system on the AT&T version. These systems are known as the System V family, because it was based on this version of AT&T Unix. Other vendors used the BSD version. Some made their own, with the goal of being broadly compatible with the two main players (System V and BSD) but each with their own specifics. A “System V operating system” is a system that is more compatible with AT&T Unix. A “BSD operating system” is a system that is more compatible with BSD.
GNU was another project to make an operating system that could play the same role as BSD: freely available, and with the same kinds of features as Unix. GNU was much more ambitious than BSD, but as a result they didn't manage to do everything they wanted, and in particular they were missing a critical bit: a kernel. In the 1990s, Linux became the de facto standard kernel for GNU, and an operating system based mostly on GNU core programs on a Linux kernel is known as “Linux”, or sometimes “GNU/Linux”.
GNU/Linux has its own history that's independent from System V and BSD, so it doesn't have all the features that all actual System V systems share, or all the features that all actual BSD systems share. Debian's bsdutils and bsdmainutils are collections of small programs that are typically present on BSD systems, but not part of the core that is present on all Unix systems.
bsdutils collection is from util-linux. They're programs with similar interfaces to the BSD utilities with the same name, but most if not all were written completely independently, and they're distributed under a GNU license.
bsdmainutils is a collection of programs copied from a BSD collection, still distributed under a BSD license. They're now maintained by Debian, but they pick up some improvements made by BSD distributions.