As everybody even down in Texas knows, PataƱjali himself doesn't seem to call the results of various saMyama_s in the third book of YS siddhi_s but rather vibhuuti_s, because the title of that book is vibhuuti-paada.
The only time the word siddhi is used in the 3rd book is the "infamous": te samaadhaav upasargaa vyutthaane siddhayaH (nominative plural from 'siddhiH'). Many modern Indian gurus, and stuff, don't know Sanskrit very well, so they seem to read that suutra in a way that in their petty minds changes the predicative at the end (siddhayaH) to an apposition, or perhaps even the subject, in that suutra. The real subject of that sentence, of course, is the pronoun 'te' that per e.g. Vyaasa and Bhojadeva refers *only* to the "divine" senses (TM: finest hearing, etc.) mentioned in the previous suutra! It seems really dense to think that PataƱjali said saMyama's are impediments to samaadhi, because the first suutra of the IV book states: janmauSadhi-mantra-tapaH-samaadhi-jaaH siddhayaH. So, *...samaadhi-jaaH siddhayaH*: siddhis are born of samaadhi (and some other stuff mentioned in that suutra)! (Perhaps the reason why Maharishi wanted to "misspell" 'siddhi' as 'sidhi' was that he didn't want to use the word 'TM-vibhuutis' even if that might have been more true to the suutra_s, probably because 'sidhi' sounds cooler, so to speak, than vibhuuti...) vibhUti mfn. penetrating , pervading Nir. ; abundant , plentiful RV. ; mighty , powerful ib. ; presiding over (gen.) ib. viii , 50 , 6 ; m. N. of a Sa1dhya Hariv. ; of a son of Vis3va1mitra MBh. ; of a king VP. ; f. development , multiplication , expansion , plenty , abundance Ka1v. Katha1s. &c. ; ****manifestation of might , great power , superhuman power (consisting of eight faculties , especially attributed to S3iva , but supposed also to be attainable by human beings through worship of that deity , viz. %{aNiman} , the power of becoming as minute as an atom ; %{laghiman} , extreme lightness ; %{prA7pti} , attaining or reaching anything [e.g. the moon with the tip of the finger] [979,1] ; %{prAkAmya} , irresistible will ; %{mahiman} , illimitable bulk ; %{IzitA} , supreme dominion ; %{vazitA} , subjugating by magic ; and %{kAmA7vasAyitA} , the suppressing all desires)**** ib. ;