Yes, Pyp is the abbreviation.
No, a different genus name (as in Pyp or Zygo) means you're talking about completely different species. That is, unless it's a renamed genus, as happened when Pyp's were changed from Onc to Pyp. Onc Mendenhall is the same as Pyp Mendenhall.
If you haven't read this, you might want to:
In orchid names, capitalization and quotes all have specific meaning.
As for culture, I give my Pyps a bit more water and humidity than my Onc's, but otherwise they're similar. Any Psychopsis gurus want to chime in...Diane?