In ICD-10 (and I believe in DSM V too), classic schizophrenia/delusional disorders and drug induced mental/behavioral disorders have a different classification status, so no, they are not the same even by the standard diagnostic manuals. Even in the section dealing with drug induce disorders, they clearly specify that to fit the classification the symptoms should not be ¨explained on the basis of acute intoxication alone¨ , which means (if I understand correctly) most transient psychotic-like symptoms in a psychedelic state would NOT fit the definition for those disorders.
Plus, of course, we can still criticise those diagnostic tools in the first place, but that´s a separate discussion.
But yes I definitely do think that psychedelics can induce experiences that have similarities to the schizo/psychotic experience. Like a venn diagram, they overlap in some areas but are not the same. Its imo innacurate and a disservice for both the psychedelic community as well as for those suffering from mental conditions to equate them completely without realizing the clear differences (but its also a disservice to look at psychedelics `romantically` and think it`s all `rosy flowers` without realizing the possibility of delusional experiences)
It´s important to know we could have delusional experiences with these substances, have temporary psychotic-like mental patterns and behaviors, and do stupid things, like run around screaming while having one`s door open with the DMT extraction equipment in plain sight. Or it could all be wonderful. Either way, be careful folks