Are the top web search engines correspondingly related to the top web browsers?

I should begin by admitting that this idea sprung up in my mind (probably) as a repercussion of my watching the movie "Chaos" today morning (there isn't much of a direct relation between the movie and this idea though).

This is pretty straightforward- the current top web search engines (Google Search, Yahoo Search, Live/MSN Search, Ask.com Search- in that order) bear resemblance to the current top web browsers (Windows Internet Explorer, Mozilla Firefox, Apple Safari, Opera Browser- in that order again) in some striking ways- apart from a broad similarity in their current market shares.

I'll list those here

1) Google Search and Windows Internet Explorer- Both these market leaders are zippy (a clean install of IE 7 runs and renders fast- and most of the complaints of IE 6 or IE 7 being slow or heavy are a result of bad add-ons or wrong settings). Both are lightweight- IE is the least resource consuming browser on Windows operating system, when stacked up against the other 3 in question here- while Google Search is the lightest web search engine out of the 4 being considered here.

2) Yahoo Search and Mozilla Firefox- Both these powerhouses pack large number of useful features, and both "get the work done", although in the process of achieving this, they tend to be heavier than their more popular rivals.

3) Live/MSN Search and Apple Safari- Slick looks mark their main resemblance, as is the tremendous promise both of them hold. Both are expected to gain market share at the expense of their larger rivals.

4) Ask.com Search and Opera Browser- "Innovation" and "Innovative features" are the hallmarks of both of them. Each one of them is an underdog, fighting for survival, constantly innovating in the process. Each of them provides innovative features and tools not to be found (yet) elsewhere.

I can even add AOL Search and Netscape Browser/Navigator here- with feature richness but undue bloat characterising them both.

The important and unresolved point, however, is- does this correspondence have something more than what meets the eye (something scientific, some patterns maybe)? Or is it merely a consequence of an unsettled mind watching a movie as confounding as "Chaos"?

If we are able to identify some common characteristics in the products and services talked about in this post (which caused them to attain their respective positions in the market), we shall be a step closer to identifying and listing "Rules for Success".

P.S.- Identification of these "Rules for Success" is an area of my interest, and I have put significant time and energy into it.