We can draw the naming conventions in most states from one single original cause. That being the Morrill Land Grant Acts. Originally passed during the Civil War, the idea was that each state would get a lump of money from the sale of federal land in that state or out west and use it to start a college. Those schools then would be required to teach 4 main areas, Military tactics(there was a war on and a need for officers!), Agricultural Sciences, Mechanical Arts, and Liberal Arts. The goal being to bring additional educational opportunities to the rural and agricultural classes.

to the endowment, support, and maintenance of at least one college where the leading object shall be, without excluding other scientific and classical studies and including military tactics, to teach such branches of learning as are related to agriculture and the mechanic arts, in such manner as the legislatures of the States may respectively prescribe, in order to promote the liberal and practical education of the industrial classes in the several pursuits and professions in life.

Previously most schools, even state ones had been the purview of relatively elite or connected interests, with a distinct focus on a liberal education. These schools also tended to be a good deal older, with many dating back to the early years of the nation. The University of Virginia being a great example here.

So then we have the problem of what to call these schools, as for the most part as you note the name of BLANK STATE University or University of BLANK STATE were generally taken. So many were named with an eye towards their mission. For instance when Oklahoma got their Land Grant school off the ground it was named Oklahoma Agricultural and Mechanical College, and only later in the 50's when the school's programs and mission had continued to expand was it renamed Oklahoma State University. OK is actually a really neat example as they founded their other 2 main schools all at the same time right before becoming a state. OU was founded as the Territorial University with a more liberal education focus, while the 3rd schools was a "Normal School" essentially a Teacher's College. So you see in just about every state the Land Grant School having a series of names or sticking to the Tech, A&M, or State monikers as a combined reflection of their original narrow focus and later expansion to broad full spectrum schools like Texas A&M, Virginia Tech, Penn State, etc.

But that also means many of the schools were starting at a disadvantage when it comes to things like endowments, attractiveness to students and donors, and focus on programs like Law Schools or Medical fields that do much to boost school rankings in the modern system. Many have evolved over the years to have those features but it hasn't been a uniform process. You also have additional rounds of Land Grant founding's when states were required to either admit Black students or found an additional school for them with the money. This then is where we get say Alabama A&M, or Florida A&M.

We can track this disparity today in hard terms in endowment numbers for instance. If we step outside the 20 year rule for a moment we can note that of the 20 largest endowments at schools in the US, 4 are State Universities, while just 2 are Land grants(one is MIT with a rather unique history or being semi independent) and the other is Texas A&M(because everything is bigger in Texas and the state has aggressively protected university funding for both UT and TAMU in their giant funds the size of some nation's GDP's). The remained then being made up of Private schools, including most of the Ivy League.

tOSU and Ohio then present a unique circumstance as you pointed out. Frankly it comes down to Ohio not having the political protection and favoritism at the state level that other flagship schools did. Rutherford B. Hayes was a major factor in founding tOSU as a new school as opposed to the route some states took(like NJ with Rutgers) of taking the money and giving it to an existing school. His clout of course would only grow in the White House, and he was not alone. That meant when it came time to appropriate state funds that the pattern of funding more programs at the Flagship vs the Land Grant was reversed.