Blake and Coleridge are linked mostly by their rejection of what came before them. Blake was an early romantic writer and Coleridge, of course, was at the heart of the romantic movement as it swept across the British Isles starting in 1798. They are similar in their rejection of virtually everything neoclassical.
Other than that, however, they are mostly different, as illustrated in the poems you ask about: "A Poison Tree" and "The Rime of the Ancient Mariner."
Coleridge is very much about imagination. For him, imagination is more than a means to an end. In some cases, it seems to be the end, or the purpose, of his poetry. "Rime" is a work of the imagination. It's a fantasy. The natural becomes the supernatural: the albatross saves the ship, killing the albatross has supernatural implications, a ghost ship avenges the irresponsible destruction of one of God's creatures, etc. Coleridge's diction, or word choice, is somewhat archaic and elaborate: "Eftsoons" is used for immediately, for instance. And poetic sound devises dominate the poem: alliteration, consonance, assonance, and internal rhyme, in addition to formal end rhyme.
Blake uses imagination as poets usually do, but imagination does not dominate and is only a means to an end. "A Poison Tree" is symbolic and philosophical and is centered by its central allusion to the biblical tree of life and knowledge. Emotions left unexpressed and psychologically held in, fester and turn to poison: Christian forbearance, the target of the poem, leads to the festering and poisoning. Oppositions are featured in the poem--revealing anger and expressing it and handling it versus withholding anger and camouflaging it and nurturing it-- to form a work more allegory than fantasy, as Coleridge's is. Blakes's diction consists of everyday language, and end rhymes, placed closely together in each stanza with an aabb scheme, provide unity and are the dominant sound device used.
Both poets reject the neoclassical, but their romantic impulses are quite different.