Ink traps are a device to compensate for over-absorbent papers and metal type in letterpress printing. They are mostly irrelevant for offset presses. James Felici has an excellent summary in "The Complete Manual of Typography" (highly recommended for anyone working with type). They are mostly irrelevant today, unless you are working on a letterpress project.
That aside, it definitely DOES make a difference which font you use at what type sizes.
Metal type, from its earliest days, was drawn and cast individually for every point size. A print shop might purchase a Caslon at 8, 10, 12, 16 and 24 points. Each character of each font was individually made. You are probably aware that characters in small sizes must be a drawn more heavily, relative to height, than at normal text sizes. Conversely, display sizes require lighter strokes and finer detail, particularly in serifs. They are not just a straight enlargement of the text design.
Better than 99% of digital text fonts are drawn for use at 12 points. As a result, they lack many nuances and fine detail at display sizes and are too light, and too tightly spaced, in tiny settings such as might be used for captions and footnotes. This was one of the trade-offs that came in with phototypesetting and was the rule in the early days (i.e., up to a very few years ago) of digital type. Hinting was a way to mitigate some of the issues created by raster-dot/character size problems on low resolution devices like laser printers, but it didn't address the fact that an outline drawn to look good at 12 points would not work well at 36 or 6 points.
The idea of Multiple Master fonts was that the font software contained different outlines that would be invoked for different sizes. It had some traction for a while, but hasn't proved workable and is fading out. TrueType Collections (.ttc) were another approach to the problem.
Display or "titling" faces, such as Trajan or Felix Titling, are specifically drawn for 24 point and up.
Today, several foundries produce OpenType versions of typefaces in a range of size-specific fonts, typically optimized at 6-8 point, 12 point, 16-18 point and 24 point, with names like Caption, Text, Subhead and Display. Using the appropriate font makes a big difference to the appearance of a typeset page. The Garamond Premier Pro family from Adobe, designed by Robert Slimbach over the course of many years, contains 39 fonts, covering several weights in each of the four size ranges, in both Roman and Italic faces, making it one of the most versatile and useful digital "classic" typefaces.
Advanced typesetting software can automatically switch to the correct optical font for the size specified, if the appropriate information is contained in the fonts themselves.
If you plan on setting a lot of type, you'll find that investing in the complete font families of a few "opticals" will be very worthwhile.