What is the relationship between capacity horsepower and compression ratio?

When you browse through cars specs you notice that for example a BMW has more horsepower than a Mazda but a higher compression ratio and such stories.
How is that?
I mean that any company can make strong cars if it raise compression ratio.

how can a company make more horsepower out of the same capacity like 2.0 ?

I CANNOT UNDERSTAND I AM VERY CONFUSED
PLEASE HELP ME

Well a combustion engine is basically a big air pump. You can also view it as a big explosion. As the air expands it exerts pressure. Light a fire cracker and it will explode but if you unwrap the gunpowder charge and light it in open air all you get is a flash. A cumbustion chamber is just that containing an explosion to to get the expaning gases to excert pressure. The more you compress the fuel air mixture in a cylinder the more volitile it becomes but when it fires it exerts more pressure on the piston which gives you more power. Many manufacturers keep the compression ratio (CR) around 8 : 1 for various reasons mainly based on the type of customer they plan the vehicle for. The higher you go in CR the more octane you have to use to keep the fuel from combusting prematurly. The added compression ratio also requires stronger parts to maintian. BMW as opposed to a Mazda is looking for the prestigious rich type person, or someone who want a performance vehicle, so they tailor their design to attract those ppl. A lady buying a minivan doesn't want to always run 93 octane, that is more money she will have to spend when she could by something that uses 87. Hope I haven't over simplified things and I hope it makes sence. Any questions just ask, I'm sure some other guys would be willing to get more detailed with it as well.