Similes and metaphors are both figures of speech. Metaphors are words or phrases that are applied to actions/objects in a way that can't be literally applicable. Similes, on the other hand, are used to make emphatic descriptions by comparing two different things and usually use the words as or like to connect both words or phrases.
In Stereo Heart, "my heart's a stereo" is a phrase that may be used to express something, but cannot be interpreted as a realistic statement. A simile that can be found on this song is "keep it stuck in your head, like your favorite tune". In this case, a comparison is made to emphasize the first phrase.
The first line of A Red, Red Rose is "O my Luve's like a red, red rose," and is a simile used to make a more vivid description of "my Luve". Metaphors can be found in the third stanza: "Till a' the seas gang dry, my dear, And the rocks melt wi' the sun." Both actions are not likely to happen, in an immediate future at least, but help express a strong feeling.