Can you give me an example of someone who has a "record of" a disability without having a current disability?

Sure. A man, who is in line for a promotion, has a history of cancer treatment, although he is now free of cancer. He is not given the promotion because his bosses are worried that, if his cancer returns, he won’t be able to do the job. He does not, at this point, meet the first part of the definition of disability because he does not have a physical or mental impairment that substantially limits one or more major life activities. However, based on his “record of” a disability, he is being discriminated against.

For additional information, take a look at the following resources:

FAQ: What are my employer's obligations after I return from medical leave? (What kind of documentation can the employer ask for when I return from medical leave?)

FAQ: What is the definition of disability under the ADA?