Good questions. Modification is often confused with accommodation, which are terms used when dealing with special education.
Modifications change general education curriculum or materials being taught. This means that students are taught something different than the other students in his/her grade level. This might look like - assignments that are not as complex, few questions to answer, or lower level text.
Accommodations do not change the general education curriculum, but help students to achieve this by teaching them in a different way or giving them extra time. Accommodations can be made in a students schedule, response, materials, instruction, test taking, or equipment.
Standard criteria probably means standard curriculum for a particular grade level. However, to be on the safe side, I would contact the school's ESE specialist for their definition.
Behavior management plans are usually put in place when the classroom teacher(s), administration, or other staff members deem it necessary. Behavior management plans come in all shapes and sizes. For example in primary grades it might be a daily behavior chart that is filled in each day by the classroom teacher and sent home for the parent's signature. If behavior problems continue, a school's or district's behavior specialist is call in for help. These plans are usually more involved and have consequences that are more severe. No matter what the behavior plan is the parents are involved.
If this doesn't answer your question complete or if you have more, please pose another one. Also, don't hesitate to contact the school to answer your questions. Many times after a parent/teacher conference, parents have question because they have had time to think and reflect. The main point here is that the school and home need to work together in order to do what is best for the child.