This is a really great question, and since I have been a school counselor, a school director, and a child therapist, I can provide some clarity.
A school counselor's role depends on your specific school. Some have academic counselors, where their primary role is to focus on academic planning, like what courses you need or how to apply to college; whereas other schools do have therapists or social workers. The difference between a school counselor and a child therapist in private practice, like me, is that typically school counselors get kids referred to them by teachers or school administration for issues that happen within school, and their job is to set goals around student behavior and school performance. For example, if a kid is having behavioral outbursts just within the classroom, a school counselor is a great fit for this; however, if kid is primarily having these outbursts at home, it's likely outside of school counselor's role. If your kid gets assigned to an evaluation to see the school psychologist, this is likely to evaluate for further educational support services, which can include special education, and can lead to either a 504 plan or an individual education plan (IEP), which are different levels of documented accommodations for your kid's learning and mental health that the school has to follow.
If your concerns about your kid are primarily within school, like their grades are dropping or they're having social skill issues with peers there, then the school counselor is a great fit for this; however, if any of these issues also present at home, like their grades are dropping because they're experiencing depression and they stay in their room all night and they’ve also lost interest in all outside activities, this is when a child therapist can be beneficial. A school counselor's role can feel limiting to only having kids on their caseload whose goals revolve around school activities; for example, a goal could be: "child will learn 2 new coping skills to use when talking in front of the class in order to reduce anxiety." A child therapist can be a bit more flexible; I can create goals like that for school plus nuanced ones for home, and also meet with the kid's teachers, parents, coaches, and outside family members, to ensure a holistic integration of these goals throughout a kid's entire life.
If you're not sure which one your kid could benefit from, I would start by reaching out to your school counselor or administration and ask what their service options are - for example, do they run groups, can they take on anyone to their individual caseload or is it limited, etc. - and then I would schedule a consult with a child therapist in order to compare services. Both child therapists and school counselors just want your kid to be thriving, happy and healthy; I will be very honest with you if I think that a school counselor is a better fit for your kid's needs than I am. Navigating these systems can be really complicated; if you’re a parent who could use some support to figure out what your child could benefit from, reach out to schedule a consult with me today.