While cosonance and alliteration are sound devices that depend upon the repetition of cosonant sounds, they differ in the placement of these sounds.
Consonance is the repetition at close intervals of the final consonant sounds of accented syllables or important words. For example, in Macbeth's soliloquy after this wife's death, he reflects that all the world is a stage upon which eacher person is merely an actor "That struts and frets his hour upon the stage." The ending sounds of the words that, struts and frets are an example of consonance.
Alliteration, on the other hand, is the repetition at close intervals of the beginning cosonant sounds of accented syllables or important words. For instance, the poet e.e. cummings makes use of alliteration to move the lines rapidly along in his poem "maggie and milly and molly and may." Here the /m/ moves the first line rapidly. Here are some other examples:mapmoon, kill-code, preach-approve.
On occasion, there is alliteration of vowels, as well. Important words and accented syllables beginning with vowels are considered alliterate as far as they have the same lack of an initial consonant sound. For example, in the repetition of the // in "Inebriate of Air am I."
Interestingly alliteration and cosonance can be combined, as in such phrases as "thick and thin," "kith and kin," and "alas and alack." These two forms of repetition of cosonants work to add sound to the reader, pleasing the ear, adding emphasis to the words, as well as advancing lines of poetry and lending to the poem structure and consistency .
Source: Literature: Structure, Sound, and Sense. Wadsworth: Cengage Learning.
Consanance is a literary device rooted in sounds. A consanant's sound is repeated 2+ times in a short phrase. Dr. Seuss used consanance in his work. For example, "Clocks on fox tick, Clocks on Knox tock." from Fox in Socks. The repetitive "ox" sound is consanance. "There's a wocket in my pocket" also uses consanance.
Alliteration is a form of consanance where the repetitive consanant sound appears at the beginning of the words in a phrase. One of my all-time favorite poem uses alliteration right in the title -- Shel Silverstein's "Sarah Cynthia Sylvia Stout, would not take the garbage out!" The repetitive S sound is alliteration.