The DNR probably use county maps printed by the State of Michigan. They have more trail detail then normal county maps do.
I believe that most or maybe all county maps have the info they use however. The State of Michigan is broken up into geographical townships and ranges. These are different than the political townships that have names.
For example: The South West corner of Houghton County in the U.P. is section 31 T47N R37W. This is read usually as Section 31 Town 47North Range 37West and consists of 36 sections within that area that are numbered 1 thru 36. Therefore when they give a location of Section xx ( 1 thru 36) Town xx North or South and range xx West or East you can go directly to a map of Michigan, if it shows counties and sections and find it without even having to know the county.
Example: Section 14 T56N R33W would be in Houghton County and contain the village of Calumet.
If you're serious about following this then you can pick up a State of Michigan Map Book which contains all of the counties and would have all the info on them.
Section numbering starts in the NE section of the township and counts backwords like this.
6 5 4 3 2 1
7 8 9 10 11 12
18 17 16 15 14 13
19 20 21 22 23 24
30 29 28 27 26 25
31 32 33 34 35 36
Each of these numbers represents 1 mile square or 1 square mile. These 36 numbers represents a town and range. Variations of this occur along irregularly shaped borders or boundries such as great lakes shorelines.
I hope you can understand the explanation.