First, Michigan does NOT issue a Concealed Carry Permit. What Michigan issues is a Concealed Pistol License and it ONLY applies to Handguns. So what's the big deal, in some states the carry permit can apply to weapons other than firearms such as Mace or a Taser.
Second, as a Michigan resident with family in Ohio I can tell you that the two state share a nearly identical list of Banned places. IIRC the most significant difference is that in Ohio you may carry into a bar as long as you are NOT consuming ANY alcohol. It's also a criminal offense to enter a posted location where in Michigan it's a Civil infraction. So, keep your eyes open for No Weapons notices. Ohio and Michigan both have a duty to notify when stopped by the police but in Ohio a failure to notify is a Felony where in Michigan it's a misdemeanor. Pay attention to that difference.
Note, whether carrying or not I always notify when stopped because it will come up if they do a records check and could result in a rather peeved police officer. It's been my experience over more that 40 years of driving that making a police officer angry will result in a ticket and making him feel at ease will often result in a simple warning. BTW, I had 4 traffic citations in the 70's, one in the 80's, none in the 90's, and one in 2014. As for warnings, I wouldn't even attempt to add them up but it's a lot. So I know from first hand experience that being friendly to the police results in much fewer traffic citations.