Upvote:5
To focus on a single type of schoolbook, we can look at the McGuffey Readers. If we look at the wiki page discussing these, we find an explanation of the progression through this series of books. (emphasis mine)
Most schools of the 19th century used only the first two in the series of McGuffey's four readers. The first Reader taught reading by using the phonics method, the identification of letters and their arrangement into words, and aided with slate work. The second Reader was used once students could read. It helped them to understand the meaning of sentences, while providing vivid stories which children could remember. The third Reader taught the definitions of words and was written at a level equivalent to the modern 5th or 6th grade. The fourth Reader was written for the highest levels of ability on the grammar school level.
You can see from this that the designation is not what you understand as 'grade' level, but is actually the individual textbooks progression level. Remember in many places in the 19th century the one-room school was the formal education system, and all the students were basically in the same classroom, so grade-level type systems were less relevant. A (the) teacher would assign students to the textbook they felt the student was ready to learn from.