This shouldn't be so hard to find but I'll be darned if I wasn't confused when I was trying to find out exactly what a "DE Safety Razor" is when I first started looking into upgrading my shaving routine.
Basically, it's probably what you're picturing: those old school razors that use razor blades that are sharp on both sides.
DE = double-edged... the razor will expose both sharp sides of the blade (which I love because I can do some passes with one side and more with the other, that remains clean).
They say "safety razor" because when these things got popular, it was a heck of a lot safer than using straight razor, you know!?
So, in review:
DE = double edged... a razor blade with two sharp sides
Safety Razor = there are protective measures built into the design so you can't cut a massive gash in your neck.
Modern cartridge razors aren't "safety razors," as we understand it because they are designed differently. They are inherently safe razors, like the DE safety razor, but the DE gets it's "safety" name in comparison to it's peers and predecessors.
Why do people freak out about DE safety razors so much? They're smooth as silk. I really can't even feel when it's cutting my hair.
The biggest lessons I have about using a DE safety razor are:
1) hold the razor at a 30 degree angle (basically a bit closer to the skin that a 45 degree angle)
2) don't apply pressure like you do to regular razors. DE safety razors don't need or want pressure. Just use the weight that is built into them
3) listen for the hair being cut (much easier to do if you move the blade a bit slower than you're used to doing with Gillettes, etc). You won't feel the hair being cut like you do with regular razors, so listening is important for me to know I'm actually getting done what I need to get done.
To really get the advantages of DE Safety razors, I highly recommend trying a whole wet shave with the soap and brush. It is truly luxurious and turns routine into relaxation.
I'll write a more detailed blog post with more lessons learned about how to make it a great shave. I feel that one of the reasons people don't switch, though, is that it can seem overwhelming at first and you wonder if you're doing it right.
There really isn't that much to is as long as you do those three things I listed above, though.
Give a DE safety razor a try! You can start for as little as buying some replacement blades at the grocery store. Why not, right!?
You'll be so glad you did.