Not sure if I should ask these questions here or in Bicycle Mechanics, but...

I'm replacing a shot, early '80s BMX headset (Tange MX-2), and I've run across conflicting statements about the 32.5 & 32.7 headset standard; are they actually the same size (as some claim), or are they really different by .2 mm?

In other words, would a "32.5" headset fit loose in a "32.7" head tube?

Also, have any of you ever used HS adapter shims? (Like, BMX 32.7 to JIS 27.0?) How well do they work?