How to refer in English to the Spanish "consonante" and "asonante" rhymes?

Verses in Spanish language can have two types of rhyme:

• Consonante rhyme, in which every sound from the stressed syllable to the end are the same.
• Asonante rhyme, in which every vowel sound from the stressed syllable to the end are the same.

A typical example of consonante rhyme would be coche/noche (somewhat similar to English rhyme light/night), whereas an asonante rhyme would be noche/doce where the vowel sounds o/e match but not so the consonant sound ch/c (it may be similar to trying to rhyme light with mind).

I have seen that in English you can talk about assonance (or vowel harmony) and consonance, but it seems to me that those terms do not refer to exactly the same idea as shown above.

So, what is the proper way to refer to the Spanish consonante and asonante rhymes in English? Or should I just write asonante rhyme? Would that be understood provided the right context?

According to A GLOSSARY OF RHYMES, you can have a perfect rhyme (true, end), which seems similar to the Spanish consonante (all the sounds rhyme perfectly), or you can have an imperfect rhyme (slant, half, oblique etc), which seems to have a broader sense than the Spanish asonante (only select sounds rhyme, but these do not have to be vowels).