mderate acidophiles with pH optima 4-5. true (or some authors name them extremal) acidophiles grow optimally at pH < 3.0 and acidotolerate have neutral pH optima and able to survive at low pH.
I went through the link you provided in response to Mr. Himanshu's question. It's very interesting. I wanted to read the whole article but I could not download. Would you please attached the pdf file of this article?
I think the information provided below may help you to get rid of the confusion
A bacterium is classified as acid-tolerant if it prefers pH above 5.5, but can grow at pH 5.5 or below, whereas an acidophilic bacterium actually experiences optimal growth at pH 5.5 or below (http://education.seattlepi.com/types-bacteria-living-acidic-ph-3540.html).
Moderate acidophiles - pH optima 3-5 and Extreme acidophiles also called true acidophiles - pH optima