My son E has a 1:1 aid as part of his IEP. This person stays by him throughout the whole school day, except when she takes a break during which time another person is assigned to just my son. E's 1:1 aid assists him with all his work, helps him form proper interactions with the other children, helps him to avoid meltdowns and agressive behaviors, sits next to him at lunch and is always within close proximity... a couple feet of him. He went through 3 1:1 aids during the previous school year, the first 2 within the first month and a half of school. His last aid was a great fit for him. She worke hard to teach him academics, social skills, on his sensory diet, with speech and more.
To me a 1:1 aid is an aid to is assigned to a specific child for a determined amount of time throughout the day.