Like the previous poster mentioned, both dilation and effacement will change how the cervix feels.
I can tell you my experience, but it may not match what your cervix does at all as the rates of the dilation and effacement can vary and don't necessarily coordinate with each other.
I dilated first. Toward the end of pregnancy, maybe around 37 weeks (ds was born at 41.4) I could feel the os open enough to sort of cup the tip of my finger (i have really skinny fingers, so I don't think it was quite 1 cm). It felt like a little divet - maybe like if you cut a piece of swiss cheese and found a hole that was just right to cover the front part of your finger maybe 1/3 of the way up the nailbed. Anyway, if you are familiar with your cervix, you'll notice this change - it's not something you would miss (although I know some people have trouble reaching their os with the belly and things moving around in there, so I guess it would be possible to feel the wrong part and think you're not dilated at all). However, if you are more effaced, I suspect the dilation would be less obvious cause the cervix wouldn't cup your finger tip like i described, but I don't know what that's like, having not experienced it.
The next notable difference was when I checked myself in active labor. It was SOOO different. The "walls" weren't as pronounced, so it was more like tracing across the surface and feeling where the edges felt different. I estimated it to be at 5cm, and I think I was right, as the midwife measured me at 7cm a couple hours later.
The last time I checked was when the baby was descending, and I had no idea whatsoever what was going on down there. I had been stalled for ages (after reaching 7cm) and all of a sudden *something* hard was up there (and not far up there by any means, like right there). I couldn't talk during labor (my brain seemed to disconnect from my mouth completely) so I didn't ask what was getting ready to come out of me, but it became obvious only when the doula (a few contractions later) observed the baby's head. I mean, duh, really, but in labor, my brain couldn't put one and one together. At that point, it was just something hard where there wasn't something hard before. I remember wondering if it was my pelvis (yet not being particularly concerned about that notion). I just knew whatever it was had to (and was going to) come out. Kind of funny in retrospect.