The Panasonic combo player/recorder you mention probably will record the tapes, but do some investigation before you buy it. Have you heard of Google? Type in the name and model number of the unit and do a Google search. You will be given many links where you can read specs, reviews, etc., and you can determine if the unit will record VHS directly to DVD.
Part two: Recording DVDs on the combo player is not the same as doing this on a computer. The Panasonic is pretty much of a one-step recording device, and your DVD will contain everything that is on the VHS. If you shot family events on tape, then there is probably 5 minutes of footage of your feet (mine have this), and this will be recorded too. A computer requires a few steps to input and record for a DVD, but the computers big strength is that it uses editing software that allows you to eliminate unwanted footage, then allows you to add transitions, add titles, add more sound, music, voice-over, etc. By the way, if your plan is to record VHS movies onto DVD, most units don't allow this. Buying a $10 DVD of the same movie is much more time and resource effective, and it's way better in quality.
Can I convert my VHS tapes to DVD by buying a combination DVD and VCR recorder? I was looking at one from Panasonic DMR-EH75VS DVD Recorder / VCR Combo with 80GB Hard Drive, HDMI, SD Card, and DV Input. Would this be the same as using a computer to convert them?