I've been told there are differences. I just haven't been told what they are exactly.

From what i know there is no difference between small hill to to big hill, mountain might be included aswell and all mountains has the same.

I think of everything as being on a continuum between plains and either forest or mountains.  The larger the forest/mountain, the more trouble that cavalry will have.  By the same token, the larger/thicker the mountain or forest, the more of an advantage that bows (on mountains) or spears and infantry (in forests) will have.

Small hills and light forests will fight a bit more like plains, while large mountains and large forests will have the most bonuses for those terrains.

the same goes for all terain types ,its all about the unit type 

cavalry doesn't get any bonus on defense on mountains. i think.. but i am pretty sure 

"Alluvial plain ( plains-jungle)" - is cavalry at an advantage (plains) or a disadvantage(Jungle) against infantry on this type of land?

To my thinking, cavalry would have the advantage of the "Plains" but would also need to have studied jungle warfare to reap the full advantage.

Can anyone explain this?

The biome modifier comes into play when one or both parties have a Warfare College in the city from which an army is sent relevant to the specific biome.  Thus if I live in or intend to fight in a jungle area I might build a Jungle Warfare College, which will give my armies boosts on squares that are labeled for that biome.

Terrain and biome are thus separate modifiers; the terrain modifier describes the offensive and defensive bonuses of the square, while the biome modifier tells you what (if any) Warfare College modifiers can be applied.  Both modifiers are used to calculate battle outcomes; the biome modifier is only used if one or both players has a specialized Warfare College in any city that has sent an army to fight on the square.

To put it another way:  Some forests are jungles, but not all jungles are forests.  (Some jungles are plains or even mountains.)  Likewise, not all deserts are plains -- some are mountains or even forests.  Arctic biome likewise contains plains and probably mountains or forests, although I'm not familiar enough with arctic terrain to be able to point to specific types.

Thank you Rill,

So there are 3 modifiers in play (Land use, Terrain and Biome) as opposed to the more usual first 2 found in the central regions.

The first two are the same as have been described and discussed in this thread - but the third (Biome) adds an extra dimension.

I took a quick look up north and out west and see it repeated for those regions as you explained.

Attacks and Raids on cities are fought on their underlying terrain.  Only raze/capture of cities is fought on Buildings terrain (when it is fought at all, which it isn't right now due to a glitch).  The other occurrence of Buildings terrain is on resource spawn sites such as Abandoned Towers.