I don't think they are necessarily different kinds of dictionaries, but is there a subtle distinction? Or maybe their etymologies?
字典 means dictionary of characters. A common 汉字字典 should contain ~8000 entries for each Chinese character. In each character entry, it's often to see example words or short phrases using that character. So, it's common to see a 汉字字典 is used as a 汉语词典.
词典 means dictionary of words. So, each entry of a 汉语词典 is a word. Generally 汉语词典 is sorted in alphabetic order in Chinese characters, so it's common to see a 汉语词典 is used as a 汉字字典.
So, in China, there's not too much difference between 汉字字典 and 汉语词典. But the book of 汉语词典 is mostly thicker then 汉字字典.
辞典 means dictionary of phrases. Generally, 辞 may refer to some famous, well known phrases said by some dead guys or famous man. Well, like I've said it's not too much differences between 词典 and 辞典, but a book of 汉语辞典 is mostly thicker then a 汉语词典. You can also expect that a 汉语大辞典 is thicker then a 汉语辞典.
In English, it will be something like:
English 字典： (26 entries)
A This is the first letter. B This is the second letter. ... Z This is the last letter.
A Indefinite article. Also the first letter. e.g. a cat. Apple A kind of fruit. Green or red. Cat A white animal. two ears, four legs. ...
Rain cats and dogs: A very big rain. Its rain drop is as big as cat or dog.
(Most 汉语辞典s include words and characters entries as well.)
词（辞）典 is for compound words, eg 成语词典、汉语词典、etc.
字典 is for Chinese characters and meanings, focus on character's meaning, may also contain related compound words.
The difference between 字典 and the other two is clear enough; the Baidu page on 字典 describes it as follows:
In the West, there is no concept of a "字典"; it is unique to China. A "字典" aims to collect 字, though it also collects words. A 词典 or 辞典 aims to collect words, though it also collects characters.
Non-Chinese languages lack a distinction between words and characters; Chinese differentiates between a 字典 and a 词典 because they have different goals.
The difference between 词典 and 辞典 is more subtle. A neither sourced nor particularly scholarly Baidu post gives the following:
A 词典 is one level deeper than a 字典: compound words and meanings; a 辞典 adds usage notes to the foundation of the 字典 and 词典.
(This same post claims that the main function of a 字典 is to provide pronunciation and writing information for characters.)