Our district is requiring staff to use specific language in our child's IEP. When I asked the teacher what the difference was between a "support person" and a 1:1, she said she wasn't sure but that's the direction they were receiving from the central office.  For example, our son has a "support person" written into his IEP for any time he pushes into Gen Ed or attends anything outside of his self-contained classroom, but a classmate specifically has a 1:1. What's the difference? Is this just legal language that allows anyone to fill in as a warm body vs someone trained to help the student?

I don't think you're going to find specific guidance about what the difference is between a support person and a 1:1 aid as those terms are not really defined in federal law. My educated guess is that typically a 1:1 aid is a particular person that is assigned to work with an individual student. A support person could be working with multiple students and may not be the same person all the time. 

I think I know the (subtle) difference.  A support person helps when needed.  A 1:1 would be by the student's side throughout the school day.  A support person could have other duties or be a 1:2 where they help 2 students at the same time.  1:1 might not have that flexibility.  If your child only needs support in gen ed, they don't need a 1:1 given this perspective.

My district will rotate 1:1 paraprofessionals where the student could have a different person in the afternoon or with a particular class.  Not sure if this is good or bad.  A consistent person would be better able to know the student and anticipate needs or recognise an antecedent and intervene before things go off track.  It might be important if a student has absence seizures which can be hard to spot.  Rotating helpers allows the paraprofessionals to have more breath of experience and learn how to support different disabilities.  Also makes the transition easier if the aide ever misses a day and the child has a sub-aide.