Since IceCreamSandwich Android has used mksh as its shell. Before then it used ash (which actually remained in the tree up to and including KitKat).
Initially Android had a very limited command-line provided by its own "toolbox" binary. These days almost everything is supplied by toybox instead.
We started moving a few of the more important tools to full BSD implementations in JellyBean before we started in earnest in Lollipop. Lollipop was a major break with the past in many ways (LP64 support and the switch to ART both having lots of knock-on effects around the system), so although this was the beginning of the end of toolbox it (a) didn't stand out given all the other systems-level changes and (b) in Marshmallow we changed direction and started the move to toybox.
The lists below show what tools were provided and where they came from in each release starting with Gingerbread. This doesn't tell the full story, because the toolbox implementations did have bugs fixed and options added over the years. Gingerbread's rm, for example, supported -r/-R but not -f. But this gives you an idea of what was available in any given release, and how usable it was likely to be.
BSD: cat dd newfs_msdos
toolbox: chmod chown cmp date df dmesg getevent getprop hd id ifconfig iftop insmod ioctl ionice kill ln log ls lsmod lsof mkdir mount mv nandread netstat notify printenv ps reboot renice rm rmdir rmmod route schedtop sendevent setconsole setprop sleep smd start stop sync top umount uptime vmstat watchprops wipe
BSD: cat dd newfs_msdos
toolbox: chmod chown cmp date df dmesg getevent getprop hd id ifconfig iftop insmod ioctl ionice kill ln log ls lsmod lsof mkdir mount mv nandread netstat notify printenv ps reboot renice rm rmdir rmmod route schedtop sendevent setconsole setprop sleep smd start stop sync top touch umount uptime vmstat watchprops wipe
BSD: cat cp dd du grep newfs_msdos
toolbox: chcon chmod chown clear cmp date df dmesg getenforce getevent getprop getsebool hd id ifconfig iftop insmod ioctl ionice kill ln load_policy log ls lsmod lsof md5 mkdir mount mv nandread netstat notify printenv ps reboot renice restorecon rm rmdir rmmod route runcon schedtop sendevent setconsole setenforce setprop setsebool sleep smd start stop sync top touch umount uptime vmstat watchprops wipe
BSD: cat cp dd du grep newfs_msdos
toolbox: chcon chmod chown clear cmp date df dmesg getenforce getevent getprop getsebool hd id ifconfig iftop insmod ioctl ionice kill ln load_policy log ls lsmod lsof md5 mkdir mkswap mount mv nandread netstat notify printenv ps readlink renice restorecon rm rmdir rmmod route runcon schedtop sendevent setconsole setenforce setprop setsebool sleep smd start stop swapoff swapon sync top touch umount uptime vmstat watchprops wipe
BSD: cat chown cp dd du grep kill ln mv printenv rm rmdir sleep sync
toolbox: chcon chmod clear cmp date df dmesg getenforce getevent getprop getsebool hd id ifconfig iftop insmod ioctl ionice load_policy log ls lsmod lsof md5 mkdir mknod mkswap mount nandread netstat newfs_msdos nohup notify ps readlink renice restorecon rmmod route runcon schedtop sendevent setenforce setprop setsebool smd start stop swapoff swapon top touch umount uptime vmstat watchprops wipe
BSD: dd du grep
toolbox: df getevent iftop ioctl ionice log ls lsof mount nandread newfs_msdos ps prlimit renice sendevent start stop top uptime watchprops
toybox: acpi basename blockdev bzcat cal cat chcon chgrp chmod chown chroot cksum clear comm cmp cp cpio cut date dirname dmesg dos2unix echo env expand expr fallocate false find free getenforce getprop groups head hostname hwclock id ifconfig inotifyd insmod kill load_policy ln logname losetup lsmod lsusb md5sum mkdir mknod mkswap mktemp modinfo more mountpoint mv netstat nice nl nohup od paste patch pgrep pidof pkill pmap printenv printf pwd readlink realpath restorecon rm rmdir rmmod route runcon sed seq setenforce setprop setsid sha1sum sleep sort split stat strings swapoff swapon sync sysctl tac tail tar taskset tee time timeout touch tr true truncate umount uname uniq unix2dos usleep vmstat wc which whoami xargs yes
BSD: dd grep
toolbox: getevent iftop ioctl log nandread newfs_msdos ps prlimit sendevent start stop top
toybox: acpi base64 basename blockdev bzcat cal cat chcon chgrp chmod chown chroot cksum clear comm cmp cp cpio cut date df dirname dmesg dos2unix du echo env expand expr fallocate false find flock free getenforce getprop groups head hostname hwclock id ifconfig inotifyd insmod ionice iorenice kill killall load_policy ln logname losetup ls lsmod lsof lsusb md5sum mkdir mknod mkswap mktemp modinfo more mount mountpoint mv netstat nice nl nohup od paste patch pgrep pidof pkill pmap printenv printf pwd readlink realpath renice restorecon rm rmdir rmmod route runcon sed seq setenforce setprop setsid sha1sum sleep sort split stat strings swapoff swapon sync sysctl tac tail tar taskset tee time timeout touch tr true truncate tty ulimit umount uname uniq unix2dos uptime usleep vmstat wc which whoami xargs xxd yes
BSD: dd grep
bzip2: bzcat bzip2 bunzip2
toolbox: getevent gzip newfs_msdos gunzip zcat
toybox: acpi base64 basename blockdev cal cat chcon chgrp chmod chown chroot chrt cksum clear cmp comm cp cpio cut date df diff dirname dmesg dos2unix du echo env expand expr fallocate false file find flock free getenforce getprop groups head hostname hwclock id ifconfig inotifyd insmod ionice iorenice kill killall ln load_policy log logname losetup ls lsmod lsof lsusb md5sum microcom mkdir mknod mkswap mktemp modinfo modprobe more mount mountpoint mv netstat nice nl nohup od paste patch pgrep pidof pkill pmap printenv printf ps pwd readlink realpath renice restorecon rm rmdir rmmod runcon sed sendevent seq setenforce setprop setsid sha1sum sha224sum sha256sum sha384sum sha512sum sleep sort split start stat stop strings swapoff swapon sync sysctl tac tail tar taskset tee time timeout top touch tr true truncate tty ulimit umount uname uniq unix2dos uptime usleep uudecode uuencode vmstat wc which whoami xargs xxd yes