"Person-first" language intends to shift the focus away from the "impairment" and towards the barriers imposed by society on people with disabilities--positioning those barriers as the problem, rather than the person with a disability. This approach was introduced in the late 1980s and was considered the acceptable approach for many years. However, some communities and activists feel this language treats disability as inherently negative.
"Identity-first" language treats disability as a diverse cultural experience and as an essential part of a person's identity. Identity-first language is used as a sign of pride by some communities, such as the Deaf community, which celebrates the unique culture developed by Deaf and hard-of-hearing people. In identity-first language, disability is treated similarly to identifiers such as race, gender identity, or sexual orientation. However, this approach may not be appropriate for all types of disabilities. People with conditions like epilepsy, for example, shouldn't be referred to as "epileptics."
Choosing to use person-first or identity-first language depends on the context and communities you are talking about. Pay attention to how people refer to themselves or (whenever possible) ask them what they prefer.
This blog post from the University of Kansas' School of Education discusses this topic in further detail.