In the United States, disability is a legal, not medical, determination. Only a judge can say for sure whether or not a person is disabled. A doctor's opinion, while an important piece of evidence, does not by itself qualify a person as disabled.
Several federal and state laws are involved in determining the rights of a person to have or be accompanied by a service animal. The definition of "disabled" in laws can vary greatly. Being considered disabled by the Social Security Administration doesn't necessarily mean a person is disabled for purposes of qualifying to use a service animal in areas where pets are not normally permitted.
Congress defined "disability" in the Americans with Disabilities Act of 1990 as follows:
(A) a physical or mental impairment that substantially limits one or more of the major life activities of such individual;
(B) a record of such an impairment; or
(C) being regarded as having such impairment.
Most, but not all, Federal and state disability laws apply the same or a similar definition.
The Supreme Court of the United States (SCOTUS) refined this definition in several key decisions, including the two below.
SUTTON V. UNITED AIR LINES, INC.
If something such as glasses or medication mitigate the disability then the person is not considered disabled under the ADA.
"A “disability” exists only where an impairment “substantially limits” a major life activity, not where it “might,” “could,” or “would” be substantially limiting if mitigating measures were not taken. A person whose physical or mental impairment is corrected by medication or other measures does not have an impairment that presently “substantially limits” a major life activity. To be sure, a person whose physical or mental impairment is corrected by mitigating measures still has an impairment, but if the impairment is corrected it does not “substantially limi[t]” a major life activity."
“The determination of whether an individual has a disability is not necessarily based on the name or diagnosis of the impairment the person has, but rather on the effect of that impairment on the life of the individual”
TOYOTA MOTOR MFG., KY., INC. V. WILLIAMS
An inability to work, or to do specific work, does not constitute a disability under the ADA. The severity of an impairment must be evaluated across a broad range of jobs or of daily life activities.
"When addressing the major life activity of performing manual tasks, the central inquiry must be whether the claimant is unable to perform the variety of tasks central to most people’s daily lives, not whether the claimant is unable to perform the tasks associated with her specific job."