Tayyip's politics could be best definied by the term "national populism". While the AKP has been, traditionally, a "big tent" party, Erdogan claims to be supported by an overwhelming majority of the Turkish people, asks for more authority in the hands of one man (namely, himself) on that basis, appeals to religious and national sentiment in the name of vaguely defined "tradition" and with a promise to restore a supposedly lost order and outside of a well-established theocratic or nationalist ideology (as would be the case of, say, Iran, or Nazist Germany), promises to uproot corruption and guarantee the welfare of all while presenting no actionable plan to actually achieve those goals. This checks all the boxes of national populism, and then some.
Of course, with Turkey being not a Western democracy made of checks and balances where the guns of the Silahlı Kuvvetleri have more weight than the rule of law, he gets to keep his demagogic promises far more easily. But make no mistake, the only reason he's not getting all chummy with Central European right-wing parties is that he appeals to Muslims while those parties appeal to Christians - which, in the frame of reference of nationalist and xenophobic politics, make them incompatible from the get-go.
P.S. the term "Islamofascism" is a misnomer.
Fascism is, essentially, an ideology that proposes to build a religion of the Nation, represented by the State; this is best expressed by the words of Giovanni Gentile (one of the fathers of the Fascist doctrine): "Fascism conceives of the State as an absolute, in comparison with which all individuals or groups are relative, only to be conceived in their relation to the State."
While the idea of defining theocratical totalitarianism as "fascism" may sound appealing, any such definition is self-contradictory. Islamic radicalism believes any temporal authority should be subordinate to the will of God and to Sharia. And I know that, especially in the English-speaking world, "fascism" and "totalitarianism" are essentially treated as synonyms, but they're not. This is important in understanding why Erdogan and the IS are not the same thing. Erdogan isn't surrendering a iota of decisional power to the Islamic clergy; the Islam he claims to protect is religion-as-a-cultural-system and not religion-as-cosmology. Compare it to the Daesh, which are led by an Imam, and believe that the end times as prophetized by Islam are near.
