When selecting a character from the Wingdings font to insert into a document, MS Word 2015 and InDesign CS 5.5 show different glyph indices for at least some characters.
According to Word, the character I am looking for, Unicode 25A0 (black square), has a decimal Wingdings gid of 110. The two online resources I found, http://www.alanwood.net/demos/wingdings.html and http://www.csn.ul.ie/~caolan/wingdings/proposal/, confirm that number. Still, InDesign displays a gid of 132.
Why does InDesign show a different gid for the same glyph of the same font?
You are confusing the assigned Unicode codepoint or character set encoding with the glyph index.
This font uses a custom character set, and it's the character n (U+006E) that actually displays a square -- not the Unicode character U+25A0. If you insert an Arial Unicode MS black square in your text and then change the font to Wingdings, you will see the character disappear.
The glyph index as reported by InDesign has nothing to do with character sets, Unicode, and anything else. This index is just an increasing number for each separate glyph in a font -- of which there may be few, quite some, or a lot. Glyph indexes always start at 0, which indicates the 'missing character' character (and so is not useful to use), and every next glyph is enumerated. This enumeration is translated to Unicode or another character mapping through a font's encoding. The enumeration in itself means nothing: a font may contain 'A', 'B', 'C' as its first 3 glyphs, or it may contain '#', '☺', 'ó', or anything else.
This glyph order is entirely irrelevant to the working of the font itself, and for all practical end-user operations you may as well forget there is such a thing. (It's something else if you try to change the font of a certain glyph -- you may get to see another character because there is absolutely no need for two fonts to have the same glyph in the exact same position.)
You are looking at the wrong place in InDesign: the Glyphs panel shows all glyphs and always shows their glyph index (because all characters have one, per definition of 'glyph index'), but only their Unicode codepoint if one is assigned.
InDesign is somewhat smarter than Word in how it processes dingbat/symbol fonts: rather than lying and saying 'this "is" the letter n', it assigns a private Unicode codepoint; in this case, U+F06E. That way you can never accidentally assign another font and get the letter n.