Generating fonts of all LaTeX math symbols

It may take more than comments to clarify some things. So here is an answer though it probably won't get what you want. Don't hesitate to ask if there are unclear points.

1. Metafonts are rarely used today. What you saw are some Type 1 variant of the AMS fonts.
2. TeX, either pdfTeX or others, don't really generate fonts. Basically what TeX know about fonts are the glyph's metrics: e.g., how large is x or A, what's the width and height and depths they occupy. In the end. What TeX see is a lot of boxes.
3. However, each box has an input encoding associated with it. So that TeX know things like "this box is an A". And when TeX generate the output DVI or PDF in the case pdfTeX, it maps these boxes to a specific font's glyphs, through the output encoding. And pdfTeX will embde those Type1 fonts. And when a PDF reader open the file, it use the embedded fonts and position information of the PDF file to draw all those glyphs.
4. So from start to end, TeX does not really generate any fonts. Sometime, when Metafont is really used, today's TeX can automatically call external program, mf etc., to generate the bitmap fonts, but still TeX only sees the glyphs as boxes.

The above explanations are not exactly how TeX works. But it shall explain how TeX sees fonts. Things like encodings has changed from engine to engine. For example LuaTeX use a font table to store the metrics information and use Unicode for both input and output.

So the conclusion is that, pdfTeX has (almost) nothing to do with generating fonts.

Therefore, I think you question can be rephrased as the following

How do I transfer the fonts used in a file to TTF fonts

1. Find the fonts. Most likely you will find many Type 1 PostScript fonts. You will not find those fonts in the PDF file generated by pdfTeX. (Not exactly, there are tools to extract embedded fonts). You need to read the source file, see what fonts are used, and find the corresponding PostScript fonts.
2. Use a font editing tool to convert those pfb files, along with their metrics (afm files), to a modern OpenType files. Free tools including FontForge and Adobe Font Development Kit. The later was designed exactly for this purpose: transfer old Type 1 fonts to new OpenType fonts.

Also, why do you want TTF instead of OTF? OTF can be used by most platforms. TTF use quadratic Bézier splines while OpenType can use the same cubic Bézier splines as Type1 fonts (the so called CFF fonts, a PostScript flavor of OTF). I haven't done any actual converting myself, but I think it shall be more natural to convert Type1 to CFF rathe than TTF. I guess you use Windows, and TTF is indeed more common there. But recent Windows support OTF as well (without ClearType obviously, which use TTF hinting explicitly)

The last, I hope I got your idea right. Do you think that because pdfTeX can generate PDF files that can be viewed by modern applications like Adobe Reader, so it must have a way to generate modern format fonts which is commonly used in today's applications? In fact, that is just a feature of the PDF file format, which allows font embedding. And not only TTF, OpenType, Type1, Type3 even bitmap fonts all can be embedded in a PDF file and be viewed by a PDF reader. To do that pdfTeX need to know 1) the font metrics 2) where to find the font files to embed.

If all you want, ultimately, is being able to input those math symbols in other applications, say Word, then you can simply use a OpenType math fonts. Freely available fonts are XITS-Math, Asana-Math, Commercial fonts including LucidaBr Math (cost 90USD) and Minion Math (something like 700EUR for a complete set, but I found it worth it). Also Cambria Math is distributed with Windows and Office (for both Windows and Mac). The last, the computer modern fonts can be replaced with Latin Modern, and Computer Modern math symbols can be found in Latin Modern Math.