What is the difference in martinis?

A dirty martini is a regular martini with olive juice added. Turns cloudy so I'd guess that's why it's called dirty. I have had them with a shake of pepper in addition to the olive juice - doesn't add flavor but really looks like dirt. (I like mine with Absoult & VERY dirty !!)

Shaken is when the ingredients and ice are placed into a cocktail shaker (roughly - a glass shaped thing with a lid) and shaken up. The drink then is poured through a filter into the glass you're going to serve it in, leaving the ice in the shaker.

Stirred is, literally, placed in the serving glass & stirred to mix the ingredients. For this, the ingredients should be chilled first imo. I drink mine shaken.

A dirty martini has olive juice in it. The difference between shaken and stirred is personal taste it's all about the dillusion of the booze by the ice, also some people believe the shaken martini "bruises" the booze.

Dirt Martini

All I know is I like the chocolate covered cherry Tini, but I found you a link that goes in to detail about each martini recipe and how different they are. And shaken means with ice in the shaker and stirred is just stirred in the glass with the olive, nothing more.

Shaking a martini does not "bruise" the gin. It simply makes it hazy or cloudy in appearance because of the cold, which can be undesirable but does not change the flavor.