A "digraph" is a combination of two letters used in writing to represent a single sound; some examples from English would be: oo, ee, ir.
A "diphthong" is a compound vowel sound made up of two different vowels within the same syllable; some examples from English are /aʊ/ as in "house", /ei/ as in "make".
The vowel of "stir/girl" is slightly different to the vowel of "mother/weather". The first, /ɛː/, is pronounced further forward in the mouth and is longer, and it is only found in stressed syllables. It can be represented in English by various digraphs, including "ir", "er", "ur", "ear" (as in "girl", "fern", "burn", "learn"). The second, /ə/, can be represented in many different ways in English, including "er"; it is shorter, pronounced nearer the centre of the mouth and is only found in unstressed syllables.