The Greek basic Unicode range (0370-03FF) originally encoded the characters required for modern Greek: the 24-letter alphabet, a couple of numerical symbols, and vowels with tonos and/or diaeresis (in addition to Coptic and a few other symbols). When the Greek extended range (1F00-1FFF) was added to handle Polytonic Greek (for both Classical and katherevousa Greek), this basically involved the addition of accented vowels, plus breathing marks, subscript iotas, etc.
For some reason, perhaps because of an oversight, or perhaps because the editors thought that there was some essential difference between tonos and oxia (acute), which there is not. Sixteen characters in the Greek basic set were duplicated in Greek extended:
|Unicode||Beta Code||Basic codepoint||extended codepoint|
There is no semantic difference between, for example, ά and ά (both alpha-oxia), so in most cases you don't need to worry about this. Your Greek Keyboards (Unicode) will make a decision and input one or the other. A search engine should be able to find both from either input (just as they should be able to strip diacritics altogether from a search term, if desired).
Most Greek Fonts (Unicode) will display both versions identically. A notable exception is Adobe Garamond Premiere Pro, which places the accent in the lower code point versions at almost a vertical angle, and the upper code point versions at a slanted, ca. 45-degree angle. This can cause a problem with software that (correctly) normalizes the higher points to the lower ones, producing an inconsistent appearance of accentuation.
There have been problems with this (certain fonts in certain browsers don't get it right, for example). It seems (see discussion from GreekKeys Unicode) that the higher codepoint, in Extended Greek, has been de facto deprecated, by virtue of Unicode normalization rules that turn the higher code point vowels into their lower code point equivalents. By preference all tools and input methods should use the Basic Greek vowel+tonos for these character combinations. Fonts and search tools should continue to support both for the sake of legacy data.