Salary chart interpretation: "M.A" vs "60 Units includes MA" vs "M.A. plus 35 Grad Units"
Are these public school districts?

 Interpreting Salary Tables

School districts often have different pay schedules, which is what you are seeing.  Although I'm not from California, I've seen quite a few of these in my own state.

"60 semester graduate units Includes M.A." likely means that she can count her M.A. credits as part of the 60 hour requirement. If her M.A. required 36 hours, she could qualify with an additional 24 hours.

I is the lowest pay scale because it requires the least number of credits. Think of it as MA+0 credits.  II is MA+35 credits; III is MA+60 credits.  Pay increases with additional coursework.

 The Rationale Behind These Tables

Primary and secondary teachers (and other staff, like counselors or behavioral specialists) often start their careers with a Bachelor's degree, which is required in most states for a teaching license.  

Additional education is desirable for teachers. It allows them to stay up to date on teaching techniques, expand their subject-matter expertise, earn additional endorsements or licenses, or earn higher degrees (which might include any of the previous reasons).  For example, a physics teacher who wants to expand into teaching biology might be required (by state law) to have a biology endorsement, which might take 12 credits to earn.

Since salary advancement is tied to having higher degrees and more college credit, it is not uncommon to see a teacher with an MA plus an additional 30-40 credits - if they are a career teacher.  These credits would have been accumulated over time, perhaps 1-2 courses a year, rather than the traditional college schedule of 4-5 courses at once. These credits may or may not be part of a degree program.  A Ph.D is less common, but does happen occasionally.