Well Jobs himself said he got the name "Apple" from the Beatles' company so arguably (at least a lawyer would) Jobs was using Apple's name and trying to benefit from the name recognition factor and perhaps confuse people into thinking there was an association where there was none. Apple records was much more well known then than perhaps now, so a case could and apparently was successfully made.
BUT if YOU sell actual apples it should not be an infringement of TM to call yourself The Apple Store, simply descriptive of the actual product: real apples grown on apple trees, which well preceded the creation of either of the other companies and their products. Neither Apple Corps or Apple Computers sells actual apples so there would be no confusion or conflict over the product (apples) being sold or the manufacturer. There is no market overlap and no trading on a known name in the same field for market advantage or consumer recognition. So you can have an apple store because you really do sell apples whereas the other Apples don't.
(At least so far I think that's the case. Sometimes this trademark stuff goes into outer space when it comes to logic and common sense. I've seen where newer national companies evidently have won suits against older small regional businesses over the use of a "trademarked" name. Regardless of who came first and thus used the name first. It does get a bit much.)
HOWEVER, if one subscribes to Genesis, God probably could sue the pants off both Apples and win (without any special interventions either, lol) for using his/her copyrighted name/creation without his/her permission. Perhaps someone could take up a class action on his/her behalf? (Do I sense a movie here? Or at least a South Park episode?
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