it seems to me that Type2 is purely Software Virtualization
Don't conflate "Type 1 vs Type 2" and "Hardware vs Software" Virtualization. In fact, there is actually a middle ground between hardware and software: There is Full hardware (HVM), "partial" hardware (PVM), and Pure Software (SW).
I'll try to clarify by expanding all 6 combinations:
Type 1 + Full Hardware (HVM) - This allows a hypervisor like Xen HVM to boot an unmodified guest OS. This is actually slow because the hypervisor must decode "telegraph messages" that the guest OS is trying to send to the hardware. (i.e. writing to the disk drive involves repeatedly storing bytes in location 0xblahblah.)
Type 1 + Paravirtualization (PVM) - This is when you modify the guest OS a little to call the Hypervisor directly for some tasks, like disk I/O. This is faster because the guest just says "here, write this page of bytes" and doesn't have to do (virtualized) I/O on each byte. You know you're doing PVM when you install special drivers. Of course, sometimes the OS has virtual drivers built in already. For example, any modern Linux kernel will switch to PVM mode at boot automatically when it detects it's running under Xen, KVM, UML, etc.
Type 1 + Pure Software (SW) - I'm not sure if this exists, but it wouldn't be that hard to build. Since software emulation is slow, the overhead of booting a real OS and running Type 2 isn't a big deal.
Type 2 + Full Hardware (HVM) - This allows you to boot an un-modified Windows under VirtualBox or KVM. You know it's type 2 when you can reboot all your Guests and still play MP3s in the background :)
Type 2 + Paravirtualization (PVM) - This happens any time you install guest drivers, or boot a modern Linux kernel under VirtualBox/KVM.
Type 2 + Pure Software (SW) - early versions of Bochs and Qemu. (Latter versions actually have hardware assisted modes too.) You can tell they are "pure software" because they allow you to run software that you normally can't run without it. (i.e. I've run Windows '95 under Bochs on an ARM processor, and I've booted an ARM distro on an x86 under Qemu.)
There is also another subject that is unlike the above:
Container technology. Containers like Docker/Rkt/LXD don't fit in the above table. Applications in Containers are ordinary programs calling the kernel in ordinary ways, no Hypervisor involved.
It's just that containers use the Kernel features of cgroups and namespaces to make an app "feel" like it's in a VM. Each container gets a 'partitioned' view of the system: It's own filesystem, it's own user IDs, it's own process IDs, it's own hostname + IP address, etc. But from the outside, you can see all processes in all containers with 'ps'.