Can I make a copy of a DVD using a cd burner like a regular music CD?
You need a DVD burner. Check 'em out at any online electronics/computer store.
Are they the same price as CD burners?
not currently, but prices are dropping. A decent one will still run you 500, and the media, that just depends where you shop. But remember, at one point, CD-R’s were $1000. So, unless you desperately want one, hold off a year, and you’ll probably find a DVD-R for $150. 
DVD-R drives are closer to $200 already. I don’t know about copying movie DVDs though, aren’t they copy protected?
You can use a DVD-R to hold a lot more data than a CD-R. A standard one holds 4.7 GB.
I’m going to use DVD-Rs to hold copies of family photos and distribute them to my brothers. That way I don’t have to send out any discs. My new system came with a program for transferring VHS to DVD, but that’s not something I need to do.
A DVD-R costs much more than a CD-R.
You could get a $40 dvdrom drive & copy the contents off it & put it onto a cd if it fits but it depends on what the dvd is.
If you are refering to that spam software going around that says it can do this with a cdrom drive, its baloney.