What's the difference between a HDMI receiver and a BD/DVD receiver for a home theatre system?

Neither are standard terms. I would assume a "BD/DVD receiver" is (probably) a all-in-one unit with a Blu-ray player combined with a receiver (an amplifier and radio tuner) and several speakers (Usually called a Home Theater in a Box (HTIB)). An "HDMI reciever" is an amateur term for a home theater or audio/video receiver (amp and tuner) that have HDMI input and output jacks.

Note that HDMI is simply a type of connection (a single jack for audio and video) needed for the highest performance of HD displays (e.g. 1080p HDTV) and HD audio from Blu-ray disks. Depending on the rest of your equipment you may or may not benefit from HDMI. There are some variations on capability, but I'm not going to go into them here ... basically you have HDMI or you don't. HDMI capability is built in and can't be added later.

Your "BD/DVD receiver" probably has HDMI connections, in which case it is also already an "HDMI receiver".

Short answer: Buy a separate receiver and speakers, not a home-theater-in-a-box (HTIB) one. While HTIB kits are generally less expensive and come with everything you need all in one box, I do not recommend buying one in most situations. HTIB kits come with a DVD or blu-ray player that also has the surround sound processor inside of it, so the speakers connect directly to the player. This is the main weakness of HTIB setups. The DVD/blu-ray player rarely comes with additional audio inputs, let alone any surround sound inputs. This means if you wanted to use your game console or cable/satellite box or even an iPod with your surround speakers, you're out of luck. Worse still, many HTIB kits use proprietary speaker connectors, meaning if the DVD/blu-ray player ever breaks, you'll end up replacing not only it but your speakers as well. Also, since HTIB kits are designed to keep prices low, they use cheap components. I guarantee you that the speakers in the HTIB kit won't be anywhere as nice as the separate speakers you're thinking of buying. On the other hand, a home theater system built around a receiver offers you a lot more flexibility. A receiver also has the surround sound processor like the HTIB kit, but also offers a variety of audio inputs, and video throughputs. True, you will have to buy a separate DVD or blu-ray player, but this also means if you decide to upgrade the player you won't have to change the receiver. Also since the receiver has additional inputs, you can connect other things to it as well, like game consoles, iPods, cable/satellite boxes, etc. The receiver can act as a central switch for your different input devices which can simplify the operation of your system. Finally, receivers use standard connectors, so if you want to swap out a component or even upgrade the speakers, it's as easy as just reconnecting some wires. In general the most important parts of a theater system are the screen (TV) and the speakers, especially the front left/right pair. A good pair of speakers will last you just about forever. A good receiver will last a good 10 years, or until you feel you need more inputs. Really, do your parents a favor and just the components separately. You will spend more than the HTIB kit, but you'll also end up with better quality components that will last you a lot longer than any HTIB kit out there.

Generally No.

The 'systems' with a skinny receiver and BluRay player built into 1 box do not allow you to swap out parts or hook up other devices.

Sony sells a lot of these glorified BluRay players with attached speakers - but they are not a more generic system that lets you swap pieces out later.