Rhyming doesn't have to be exact, like "cat and bat." Rhyming like that is a classic way to rhyme, but there are other ways to rhyme also.
Perfect rhymes: Like my example above, end rhyming is when the last word of a line rhymes with the last word of another line, like in "The Night Before Christmas."
Twas the night before Christmas, when all through the house
Not a creature was stirring, not even a mouse.
The stockings were hung by the chimney with care,
In hopes that St Nicholas soon would be there.
Obviously this example is a poem, which is different from lyrics, but I'll explain the differences and similarities of poems and lyrics in another post.
Internal rhymes: This is when you rhyme two words within the same line. In Eminem's "Ricky Ticky Tock" he uses internal rhymes as well as end rhymes.