What browser runs on Android? It is Chrome or a modified version of it? Also, as a side-note, how can I open site shortcuts saved from Internet Explorer on Windows to the SD Card with the browser?
There's a similar question here: Which is the Android's default browser?.
The web browser utilizes WebKit for rendering. WebKit was originally forked by Apple from the KHTML rendering engine, which powers the Konqueror web browser/file manager. The WebKit engine has been open source from the beginning and is used in many browsers including Apple Safari, Google Chrome and a few other smaller browsers.
However, I disagree with the previous two answers above. Chromium is the open-sourced code base from which Google Chrome is derived, but I believe the Android browser has it's own codebase. I do not think the Android browser derives from Chromium, which contains code for integrating with window management, tabbing, extensions and many other features that are well-suited for a desktop experience.
Browsing on a mobile phone is a different experience and I believe that Google Android Browser application is NOT derived from the Chromium code base directly, though it does implement components that are built into Chromium as well.
Every version of Android has a "android browser" that is basically a cut of the open source Chromium browser. For example, the Android Browser that lives in the AOSP v4.4 (kitkat) is based on the same code as Chrome v30.0.0. Applications that use WebViews use this Android Browser (not the user's default browser).
It is an Android version of Chromium, which is what Google built on top of Webkit. The browser we call Chrome is built on top of Chromium with separate versions for Windows, OS X and Linux.
Some functionality was removed or slimmed down for the Android version.
It's similar to Safari and Mobile Safari in the sense that much of those apps code are Webkit, and on top of Webkit there's similar/identical code between the two, but they also have many parts of the code that are completely different.
Google was just up for Open Sourcing Chromium