Is an FMLA "serious health condition" the same as an ADA "disability"?

No.  An FMLA "serious health condition" is not necessarily an ADA "disability."  An ADA "disability" is an impairment that substantially limits one or more major life activities, a record of such an impairment, or being regarded as having such an impairment. 
 
Some FMLA "serious health conditions" may be ADA disabilities, for example, most cancers and serious strokes.  Other "serious health conditions" may not be ADA disabilities, for example, pregnancy or a routine broken leg or hernia.  This is because the condition is not an impairment (e.g., pregnancy), or because the impairment is not substantially limiting (e.g., a routine broken leg or hernia).
 
In addition, the fact that an individual has a record of a "serious health condition" does not necessarily mean that s/he has a record of an ADA disability.  Under the ADA, an individual must have a record of a substantially limiting impairment in order to be covered.
Finally, just because someone has a "serious health condition" also does not mean that the employer regards him/her as having an ADA disability.  To satisfy this prong of the ADA definition of "disability," the employer must treat the individual as having an impairment that substantially limits one or more major life activities.
 
To determine if an individual has an ADA disability, all pertinent evidence, including any information about whether the individual has or had a "serious health condition," should be considered.
 
Under the FMLA regulations, employers must allow EEOC investigators to review pertinent FMLA medical certifications and recertifications, and other relevant materials, upon request.  https://www.eeoc.gov/policy/docs/fmlaada.html