Morph: an actual form used as part of a word, representing one version of a morpheme.
Ex:
the form cats consists of two parts, /kæt/ + /-s/, with a lexical morpheme (“cat”) and an inflectional morpheme (“plural”).
The words dogs and horses also consist of two parts, /dɔɡ/ + /-z/ and /hɔrs/ + /-əz/.
Allomorph: one of a closely related set of morphs.
Ex:
/-s/ (“cats”), /-z/ (“dogs”), /-əz/ (“horses”)
word like sheep, so that the plural of sheep can be analyzed as /ʃip/ + /⊘/, adding another form (/⊘/) to the set of allomorphs of “plural”.
Special cases, we could propose that there may be a “zero-morph” involved when we add the “plural” morpheme.