Under Ohio's first constitution, in effect from 1803 to 1851, the presiding officer of the senate was called the speaker.
Starting in 1851, when the second constitution took effect, a new office of lieutenant governor was created.
The new position of lieutenant governor carried with it the office of president of the senate, and was nominally the presiding officer of the senate.
At this time, the duty of presiding over the senate was removed from the lieutenant governor's portfolio and the majority party of the senate began electing its own president starting in 1979.
(At this time, the nominal presiding officer of the senate was the Lieutenant Governor of Ohio.)