There are two types of "pure rhymes" and words—"masculine" and "feminine." The determining characteristic between the two is whether the most accented syllable (also called the "tonic" syllable) is the LAST syllable.
If it is, the word and rhyme are masculine. Otherwise, it's a feminine word and rhyme. Masculine words and feminine words, in "classical" or formal rhyming, NEVER rhyme with each other!
In either case, in order for two words to be a pure rhyme, they must have identical vowel-based rhyme sounds in the tonic syllable. Moreover, that tonic syllable must start with a different consonantal sound. For instance, "love" and "dove" rhyme; "ove" is the identical vowel-based rhyme sound (the vowel being "o") and "l" and "d" are the different consonantal sounds.
The rules for a feminine rhyme are the same as for a masculine rhyme, but there is an additional rule: what follows the tonic syllable must be identical. For instance, in the case of "maybe" and "baby," the "be" in maybe" and "by" in "baby" are identical in pronunciation.
"End Rhymes" are words that have a pure rhyme on their last syllable only.
"Near Rhymes" are words whose tonic syllables "almost" rhyme. That is to say, rather than having an identical vowel-based rhyme in their tonic syllable, the vowel-based rhyme is close but not perfect. For instance "toad" and "go" or "go" and "goat." There are three ways to make a "near rhyme": by subtracting a consonant after the vowel-based rhyme as in the toad/go case (where we dropped the "d' (note the "a" is silent)); adding a consonant as in the go/goat case (where we added the "t"); and finally, varying the consonant as in the case of "toad" and "goat."
"Near End Rhymes" are words that rhyme on the vowel-based rhyme sound of the last syllable only (for instance: "maybe" and "eat").
"Mosaic rhymes" are rhymes made up of more than one word. For instance, "jealous" and "tell us" or "shakey" and "make me."