What is the difference between someone with learning difficulties and mental problems?

Type of problem. Learning disorders relate to specific areas of function such as reading or math in which the person has greater difficulties than expected for that person's overall intelligence. Mental problems refer to behaviors and feelings such as depression, anxiety, adhd, severe tantrums, etc. One certainly can have both.

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What is the difference between someone having learning difficulties and having mental health problems?

These often overlap. Mental health (mh) diagnoses include learning difficulties (e.g. Adhd), but many other mh disorders can cause learning problems, e.g. Concentration/memory impairment is a symptom of depression. Though in my mind, subnormal IQ is not a mh disorder per se (though the dsm includes "borderline intellectual functioning"), it does explain most of what we label as "learning difficulties" in children. Read more...