Until a few years ago, Apple and Google were not in competition at all.
Now, mostly because Google keeps doing more and more things, they are increasingly competitors.
Here’s the latest: Google bought Motorola’s cell phone business. That puts them into direct competition with Apple’s iPhone business.
So now they are competing on browsers, computers (at least theoretically, with Google’s Chromebooks), mobile operating systems, cell phones.
All we need is for Apple to go into the Search business.