The distinctions might not be easy to find, but these 'higher order' signs are generally assumed to be either different diphthongal versions, or those with an aspirated consonant.    From Wordnik.com.  [New info on 'lily'] Reference

During the greater part of this period, also, the diphthongal vowels ae are written separate.    From Wordnik.com.  [The Catholic Encyclopedia, Volume 11: New Mexico-Philip] Reference

In the speech of many, perhaps of most, Americans there is scarcely any trace of diphthongal quality in the sound.    From Wordnik.com.  [Chapter 7. The Standard American Pronunciation. 2. The Vowels] Reference

Latin and was much more conservative of diphthongal sounds; it also used double consonants, which old Latin did not.    From Wordnik.com.  [The History of Roman Literature From the earliest period to the death of Marcus Aurelius] Reference

Many of the phonological maps show a number of different forms, e.g. Phl49 house not only shows the undiphthongized vowel but many different diphthongal forms.    From Wordnik.com.  [VERBATIM: The Language Quarterly Vol V No 4] Reference

” 29 But in British speech a greater variety of diphthongal shadings occur, “some of them familiar in the exaggerated representations of Englishmen and their speech on the American stage.    From Wordnik.com.  [Chapter 7. The Standard American Pronunciation. 2. The Vowels] Reference

British Museum, also numbered 2,764, stated to date back to 1412, can scarcely be older than 1440 or 1450, from the diphthongal writing, first introduced by Guarino of Verona, who died in 1460.    From Wordnik.com.  [Tacitus and Bracciolini The Annals Forged in the XVth Century] Reference

Owing to the trilled quality of the liquids l and r, long u after them in the same syllable does not take its full diphthongal y sound (as in cube), but more nearly that of long oo, with the modification, in the case of l, to which we have alluded.    From Wordnik.com.  [The Standard Speller; Containing Exercises for Oral Spelling; also, Sentences for Silent Spelling by Writing from Dictation. In Which the Representative Words and the Anomalous Words of the English Language are so Classified as to Indicate Their Pronunciation, and to be Fixed in the Memory by Association.] Reference

14 An example of the first type of change is the passage in English of all old long i-vowels to diphthongal ai via ei.    From Wordnik.com.  [Chapter 8. Language as a Historical Product: Phonetic Law] Reference

Other combinations are not diphthongal.    From Wordnik.com.  [The Lord of the Rings]

The proper diphthongal sounds.    From Wordnik.com.  [English Grammar in Familiar Lectures] Reference