hypervisor is an abstraction layer provided by the OS to provide virtualization. Virtualization usually require hardware support. It could require the CPU to support VTx. Virtualization is a heavy ceremony as almost everything you can enumerate is running separatedly. Another kernel is running in parallel to another kernel.
container is an applicational abstraction of isolation. Isolation can be process-isolated or hypervisor backed. An example is Windows container can run on top of hyperV or process isolation that must run the compatible kernal version with the host system.