Hello! What are “person-first language” and “identity-first language”? Which one should I use in service?

No problem.

Thank you so much!

For a long time, the gold standard in the disability field was person-first language. As the name implies, a person's first language emphasizes the personhood of the individual you are talking about and suggests that disability is just one part of a person's identity. For example, rather than saying "a disabled person," you would say "a person with a disability." Instead of talking about "the Down Syndrome woman," you would say "the woman with Down Syndrome." For many individuals, a person's first language is considered the most respectful choice. Other people with disabilities prefer identity first language. These advocates stress that disability is an important and valuable part of a person's identity, and there is nothing disrespectful or wrong about putting disability first. For example, someone diagnosed with autism spectrum disorder may prefer to be called "autistic" rather than "a person with autism."
So, if some people prefer identity-first language and others prefer person-first language, which should you use? Ultimately, the best option is to ask your client which language they prefer. People with disabilities are the experts in their lives, bodies, and experiences, and they get to make all decisions about their care, including what language should be used to refer to them.