First of all, “traditional” does not have a set of rules. To be traditional basically means “the shul I don’t go to is Orthodox.” IOW, Orthodox hashkafically but don’t keep halacha 100%. Modern Orthodox is something else, or to be precise two somethings else.(Yes, haifagirl, that is 100% grammatically correct.) There is a Modern Orthodox hashkafa that emphasizes the value of certain parts of the secular world as useful for avodas Hashem. Most of the Rabbi-Drs. with phd’s adhere to this hashkafa regardless of their dress code.
Most hashkafically Modern Orthodox Jews also never accepted the current interpretation of the phrase “daas Torah.” They still consider rabbanim to be scholars of halacha who may have special siyata dishmaya in psak beb’chinas dayan hadan emes l’amito but not necessarily have ruach hakodesh in other matters. When Rav Lichtenstein, for example, says “I’m not a navi” they believe him. As far as I can tell, that is the main sticking point in hashkafa between Modern Orthodox and charedim. The charedim see the MO as not giving proper kavod to talmidei chachamim and the Modern see the charedim as ascribing too much power to human beings. I hope I represented each hashkafa accurately without saying anything objectionable about either one.
There are also people who, regardless of hashkafa are modern in practice. They may follow either charedi or MO hashkafos philosophically but are more modern in their choices of dress and entertainment.