Students who are eligible for IDEA and Special Education are also covered by "Section 504". Section 504 is a Civil Rights Law, whereas IDEA is an educational law. However, an IEP has all the basic elements of a Modification Plan, plus some very specific features required by IDEA. If an IEP is in place, there is no need for an MP, too.
However, as a parent, you have the right to refuse Special Education Services, for any or no reason at all, even in the face of strong evidence that your child would benefit from those services. In that case, you may want to go with the Modification Plan.
Another big distinction is that Special Education is federally funded (in very complicated ways), while Modification Plans are not funded. In some districts, schools have a financial incentive to find your student eligible for IDEA, so if school staff says your child does not need an IEP, they probably do have the best interest of your child in mind.
Having a diagnosis is only part of IDEA eligibility. The team also needs to reach a consensus that the child needs specially designed instruction to benefit from a Free and Appropriate Public Education. That may be what the psychologist meant.
The educational decisions that the team makes should be based on the actual needs of the individual student, not on the diagnosis or IDEA eligibility category. I've seen appropriately placed students with ADHD (or on the autism spectrum, for that matter) with IEPs, with MPs, or with no plan or eligibility at all.
I'm not big on bombshells, personally. My ideal meeting is boring and predictable--not to mention short--because everybody knows what is going to happen ahead of time. But surprises do happen, and sometimes I go into a meeting truly on the fence, waiting to see what the other members of the team will have to say.
If you do not agree with the eligibility decisions of the team, you do have several steps you can take. One of my favorites is the help of a Disability Rights Advocate. Some of the others should be outlined in the document you received at the time of the Evaluation meeting.