Is peroxoborate and perborate the same thing?
This is necessarily  not  a chemistry answer but is a continuation of aventurin's answer.



Google ngram viewer is an online search engine h  that charts frequencies of any word or short sentence found in the sources printed between 1800 and 2012 in American English, British English etc.



So, here is the Google ngram for peroxoborate and perborate. 


So, you can see that perborate is more often used than peroxoborate. Though, the correct name (IUPAC name) is tetrahydroxidodi-µ-peroxido-diborate, people often mention the compound sodium perborate. Sodium peroxoborate seems to be obsolete.