The first is BYOM - Bring Your Own Mac. You pay for your own Mac, and they'll give you the corporate Windows image on your choice of a VM or on the hardware for you (not sure if it's via Bootcamp or complete system wipe). Your cost center incurs a surcharge for Mac support, and you can't take it to the local PC service center for most things.
The second is BYOD, and has 2 parts - phones/tablets, and laptops.
You can buy and bring any laptop you want, and we'll install the IT image, put on full disk encryption, etc. There's no subsidy for both BYOM and BYOD. You just get to chose what hardware you wanted to run with. I'm not sure if there's a requirement to buy $OURPRODUCTS, but the employee hardware discounts from Dell, Lenovo, etc only apply to them, so most people end up with our hardware. I think the largest increase in BYOD was after the Ultrabooks came out, but before they were available as a normal hardware refresh option.
You can bring your own phone or tablet. I don't know anyone with their own tablet, but the phone is popular. Very few people actually have corporate cell phones, but you can get a discounts on plans and select phones. If you bring your own phone, you grant IT remote wipe privileges in order to get the calendar and email, and a couple dozen apps.
If you Google for the company + BYOD, you'll find a lot of literature on the program; we're actually pretty open about it.