I am wondering if this is a bug or not.

When I slide down a wall or steep embankment, health quickly depletes, or I die. I wish I had a photo or demo of this to better illustrate my point.

You were playing in Realistic mode, where falling can hurt you.

I know that.

I'm saying that sliding down a embankment can hurt you, where I don't think it should.

Realistic mode is meant to be realistic, and if you fell down a steep hill, or slid down it, especially cement or dirt, you would receive large cuts, gashes, and scrapes, and in some cases bone fractures which could lead to death (bone fragments splitting, and stabbing into your vital organs) ((Yeah, I know that's really stretching it, but hey, it could happen!)).

It's part of the realistic mode, not a bug.

I think there should be some changes, like grass for example should do less damage than a huge rock.

Tek, that'd be an improvement, not something that belongs here.

The fall damage in realistic used to be a lot worse and I don't really see a problem in it right now unless I'm missing something.

This is a problem. Its a bug in the fall damage of realistic, and it happens a lot in maps like ctf_crashed that have big falls with vertical walls. If you graze the wall, it will often kill you before you are barely out of your spawn, and it can be quite irritating at times.
Considering that its not the intended behavior of the falling-damage system, this is technically a bug that has just never been fixed. (Been around forever)

What autocrat says makes sense. I have this problem lotsa times on RS when i scrape the walls, but when you fall down and scratch a vertical wall in real live, you probably get lotsa cuts and other injuries which could eventually kill you.
Maybe its not intended but still, it adds some realism.