Twenty pages, grouped by what you are looking for
Marks and signals: check mark symbols (7 characters — ticks, crosses and the three ballot boxes) and arrow symbols (90, from the four plain directions up through the doubled, hooked and barbed forms).
Hearts, across four pages because people arrive wanting four different things: heart symbols is the base set of 8; black and white heart symbols narrows to the filled and outline pair and their heavy relatives; tiny heart symbols is about which of them render small; heart symbol in text and HTML covers entering them in markup. Eight characters is the whole BMP repertoire, so those pages overlap by design rather than by accident.
Belief and meaning: cross symbols (28, from the Latin cross to the Syriac and Maltese forms), peace and wellbeing symbols (12, including the four Om characters, which are letters rather than symbols).
Sky and weather: weather symbols (27), sun, moon and planet symbols (39, including the planetary signs), star symbols (34) and flower symbols (7).
Games: card suit symbols (8 — four suits, filled and outline) and chess symbols (12, six pieces in white and black).
Reference and typography: copyright and trademark symbols (5), roman numeral symbols (40), line and box drawing symbols (90), shape symbols (90), accented and foreign characters (90) and aesthetic symbols (66).
Two characters can draw the same shape
♥ is U+2665 BLACK HEART SUIT, from the card suits. ❤ is U+2764 HEAVY BLACK HEART, from the dingbats. Both are hearts and they are different characters with different East Asian Width: U+2665 is Ambiguous, U+2764 is Neutral. The same split runs through the stars, where U+2605 BLACK STAR sits beside U+2B50 WHITE MEDIUM STAR at a different width again. When two references disagree about "the" heart or star, compare the codepoints: they are describing different characters.
The precomposed ones are single characters
Ⅳ is U+2163 ROMAN NUMERAL FOUR, one character, not the letters I and V. é is U+00E9 LATIN SMALL LETTER E WITH ACUTE, one character, not an e followed by a combining accent. Both have multi-character equivalents that look identical and compare unequal, which is why a search for one form misses text written in the other.
Where the other two wings are
Music symbols covers the seven music characters that paste, and maths and science symbols covers the operators, Greek letters and comparison signs. The index carries a sample from all three.