I can only speak to American schools, and the general gist is yes, you're right. The experiences of children with disabilities in the 1800s were highly idiosyncratic based on a child's identity - race, gender, religion, class, the nature of their disability, etc. - and where in the country they lived. The white son of a well-connected New England family likely had access to the private tutor (or multiple tutors) who could meet him wherever he was intellectually and move him towards where he needed to go at the pace at whatever pace he wanted to - or pay for the child to be cared for someone in a particular setting, effectively removing him for the family. A Black girl in the American south with a disability from a family with limited means may have struggled to gain the skills necessary for independent living - or could have been surrounded by a family who made sure she got the skills or help she needed at every stage of her life.

It's worth stating explicitly the history of education for Deaf/hard of hearing, Blind/visually impaired, Deaf-Blind, physically disabled, and cognitively disabled children all followed their own paths, often related to their parents' ability to advocate for their children and access to services or those in positions of power who can create services. If the documentary Crip Camp hasn't crossed your radar yet it's worth checking out as it provides a great overview of the shift in the disability rights movement in the latter half of the 20th century.

But back to the 19th century. In this answer to a question about toddlers and temper tantrums in the medieval era, I laid out some context related to how adults viewed children's behavior and the shifts and changes in what's considered typical and/or normal and what's considered atypical and/or abnormal. Such definitions are shaped by adults' notions about acceptable behavior, which in turn, shaped by the culture around them.

To borrow from my older answer:

I can rattle off anecdotes I've come across from teacher journals from the mid-1800s where a child is described as misbehaving (her words), but the child’s age is often not noted (“the youngest Smith boy”) or is described in the context of when they attended school (“winter session.”) However, I also know that her journal writing is informed by the social pressure she experienced related to how well she did her job. So, it's difficult to know for sure if what she's describing as "misbehavior" was the sort of thing children did because they're children or truly something dangerous or harmful. And to complicate it, the same teacher might write home that the same child was an absolute hellion to her but through sheer force of will and motherly instincts, she was able to calm him down and teach him his letters. And oh by the way, if the school board was interested in buying new books for the school, she knows this particular boy simply loves to read. Which is to say, she's a bit of an unreliable narrator with regards to the things children in her charge did. So, if you asked, "have 7-year-old boys always hated school?" I couldn't say for sure. I could tell you there are instances of teachers reporting boys around age 7 or so did not like doing the thing they asked them to do.

What this means in terms of your question is that even if a teacher in the 19th century wrote about a child who was struggling to read or follow the rules of school, the nature of social pressure around teachers meant she would likely minimize such struggles in her writing or letters home so that it didn't look like she was failing to do her job. At the same time, a teacher's journals may describe a behavior that, through a modern lens, reads like it describes a typical behavior exhibited by someone with a particular disability but the person at the time wasn't writing with that lens in mind.

The phrase "retrospective diagnosis" was coined to describe people looking at the historical record and trying to diagnosis someone. The autism community, in particular, has pushed back against efforts to identify historical figures as being autistic as such diagnoses misrepresent what it means to be autistic or have a disability. Activists remind us that the nature of disability is such that the issue doesn't reside with the person, it's the fact their society or environment isn't easily adapted to them. So two people could present with the same bodies in two different societies and communities and be seen as "disabled" in only one of them.

Finally, although most states had compulsory education laws by the 1920s or so, the laws formed only half of the equation necessary for universal education. Parents were required to educate their child but until 1954, American white public schools could refuse to provide a seat to a Black child, even if the child lived next door to the school. Until 1975, schools could likewise refuse to seat a child of any race with a disability. This didn't mean they refused all children with disabilities, but rather, if a child's behavior was deemed too [insert adjective here] for public school, a school could legally speaking, turn a child away. In places where state or local laws prohibited such actions, the social pressure on parents of children with disabilities could be intense. At the same time, the employment options available to someone who lacked a formal education were much more extensive than they are now.