Yeah the first thing you’ve gotta fix is the terminology. You’re not burning in SD or HD, you’re burning to DVD and Bl-ray. I can stick SD footage on a blu-ray and it’ll play in SD, but it’s still a blu-ray disc and won’t play in a DVD player.
So no, there is no such thing as a DVD burned in high definition, you will need a blu-ray burner, bd-r’s and a blu-ray player. Anyone you give the disc to is going to need a blu-ray player. If what you need are DVD’s then you’re stuck with standard definition and need to find a way to make the DVD look as good as possible. Make sure that if the project is less than an hour you’re using a decent bitrate like around 8mbps.
As a side note, if you are considering a blu-ray burner for your pc, be aware that you can buy units that will burn blu-rays and dvd’s, or ones that will only burn blu-rays that are normally less expensive.