They're the same to me. They both use the same DVD-RECORDABLE media, among other features. Though I am not sure if standalone DVD recorders can use the same DVD-RE-WRITABLE discs
Some stand-alone DVD and CD recorders have built-in hard disks. DVD-writers in PCs use the PC's hard disks. I've come across some early DVD recorders with somewhat limited functionality. Perhaps the newer ones aren't as constrained. DVD recorders, OTH, blend quite nicely with other AV boxes in their AV rack and are relatively easier and more user-firendly to use. Recording and transcribing from your VHS machines can be a snap and go real-time. While in PC, you have to get a separate Video capture card to transcribe. I am not sure if those DVD recorders can rip DVDs though. OTH, there are so many freeware that can in PCs, macrovision and region code notwithstanding.
I guess it all depends on your purposes. A home DVD recorder will act like any VHS recorder does. If all you want is record private videos and cable channels on DVD, they will do a perfect job. I am just not so sure about their ability ripping DVDs, which PCs can do.