Is the MAC address of my VM different to the MAC address of the host?

My landlord provides my connection to the internet and they are changing their network which requires me to register my iPhone and MBA. The instructions require me to use my MAC address at some point in the process. I run a VM using Parallels and all my mail goes to MS Outlook.

Do I provide them with the MAC address from the VM (Windows 7) or from Mountain Lion? Might they be the same?

The VM will use a virtual MAC address to map to the physical device MAC Address. Keep in mind that if you provide the MAC Address of the Wi-Fi Adapter from your MBA, that you're now locked to using that device for connectivity. Thus, your VM will need to use that device as it's bridged connection to the internet.

You should provide the physical hardware MAC address to allow your device and your VM access to the internet.

I would have written this as a comment if my user status would allow me to. This is an addition to what james_fuller already explained:

You can connect to your VM to your host's NIC. It's like your host OS becomes a router for your VM. Thus your landlord's network won't see your VM at all but only your registered MacBook.

Read about Shared Networking in this KB entry: Parallels KnowledgeBase

You can enable Shared Networking in the preferences of your VM, a restart of the VM might be necessary.

Regarding your other question:

Do I provide them with the MAC address from the VM (windows 7) or from Mountain Lion?

MAC addresses are supposed to be unique and having two identical ones in one network would cause some trouble, as ethernet packets aren't transported to an IP, but to a MAC address. A switch for example wouldn't know where to send it's packets and bot MACs would receive only parts of the data.