The source of this problem is malformed font files. The internal names of the fonts are in conflict and the flags that indicate connections between the different font files in a typeface family (Regular, Bold, Italic, Bold Italic, etc.) are missing.
The terminology is awkward. Technically and historically "Foo" is a typeface and "18 pt Foo Bold Condensed" is a font, but in the era of personal computers the definitions have blurred: a typeface is now often referred to as a "font" (even though you'll buy a particular style of that typeface as a "font" in any online store), particularly among non-typographers. The variations tend to be called "styles." People coming newly (last 25 years or so) into design are so used to scaling a font in software that they forget every size of every style of a typeface was once drawn and made individually.
For a regular application (non-professional) to give you the usual "Regular, Bold, Italic, Bold Italic" choices, the font files themselves must be individually named internally and the fact that they are associated is a specific internal flag. It's these internal flags that allow you to create bold or italic text with a keyboard shortcut or style dropdown -- the Foo Bold font file tells the OS "I am the Bold version of Foo," and so on.
You have a situation where all the individual font files have the same internal name, so Windows can't differentiate them. You see exactly one font (style) in a family; delete it, and you see another one, and so on. In Word, Open Office, etc., that's probably all you'll see. (Arial Narrow famously suffered from this problem because of an error in creating the files -- it just wouldn't show up at all, or would never show up as an available style for Arial.)
Most non-graphics applications natively understand only the usual four fonts in a family. Additional members (narrow, thin, black, extended, etc.) show up as separate typefaces.
More sophisticated applications such as Photoshop or InDesign know how to read the association flags in a set of font files and can display all the variations in a single dropdown. Garamond Premier Pro, as an example, has 39 font files in four optical sizes -- caption, regular, subhead and display -- that all show up in a single dropdown if and only if the files themselves contain the correct internal information. The ones you are having trouble with do not.
The most common source of the problem you are seeing is conversion utilities that don't do a proper job of taking older or other-platform files and turning them into well-formed OpenType or TrueType files. This often affects (illegal, it must be said) Mac --> Windows conversions, because on Mac OS the font information is split between a visible file and a hidden one. If the conversion utility doesn't correctly parse the hidden file, you get a malformed OpenType or TrueType font file that won't work properly on either platform.
Very old and "freebie" font files that are incorrectly set up internally can cause the same issue.