Meltdowns are like tantrums, only due to sensory overload or under/overstimulation. They happen when the autistic person is unable to stim to calm him/herself down.
A manic fit/mania is usually due to bipolar (not always; I have them) and it involves rapid, pressured speech, grandiose ideas, etc. It is different than a meltdown because there is less crying and more hyperactivity.
Sometimes, medications that doctors prescribe for autism, bipolar, or other mental illnesses can cause one or both of these phenomenon.
Hope this helps! 
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Diagnosed with Aspergers, ADHD, Bipolar Type II, OCD, and generalized anxiety.