It is by no means a question of terms. A state may have a president elected even by parliament or by public ballot, but not in reality be presidential. It is essentially a question of which authority forms the government. If it is the president, we are dealing with a presidential system. If the said right is accorded to parliament, this is a parliamentary republic, regardless of whether it has a president or not.
Legal niceties play no part here.
From the formal viewpoint, the fundamental, albeit not absolute, principle of the separation of powers is violated in a parliamentary republic, since the executive is wholly dependent on the legislature. The formal aspect would be of no significance, of course, were it not for the negative influence of this dependence on the viability of the system of government and the efficiency of the activity of the legislature and the executive. No one could, of course, deny the viability of a parliamentary system, but no one could deny either the fact that the parliamentary system is viable only in states in which one or, at the most, two or three serious mass parties, each of which is capable of forming a parliamentary majority and, thanks to this, ensuring the effective activity of the government, has taken shape historically. In the event of the election of patchwork, multiparty parliaments, the parliamentary system leads to the formation of a weak coalition government and incessant internal upheavals, which very often end in coup, tyranny and, frequently, outside interference. In the event of a parliamentary system being established, the same sorry and disastrous fate, I profoundly believe, awaits Armenia because one, two or three mass parties could take shape here in a dozen years, at best.