Bochs is a powerful x86/amd64 hardware emulation and debugger software. Besides the CPU and instruct set extensions, it simulates common PC/AT hardware, an ISA and PCI system bus, memory, disks, video hardware, ethernet, and enough of a compatible BIOS to run DOS/Winows, Linux/BSD, Minix and other operating systems. It doesn't provide virtualization, thus runs extremely slow, but is safe to run for the host operating system.
QEMU is a generic machine emulator and virtualizer. It can emulate other CPU and host architectures, or run native binaries with native performances by executing the guest code directly on the host CPU any only emulate devices. It's thus often used in conjunction with KVM on Linux for system virtualization.