Is ES Fuzzy Query Symmetric

Question

Is Elastic Search Fuzzy Query symmetric?

For example if I have:

Setup1
Index Documents = ["hat", "funny"]
Queries = ["cat", "bat", "monkey"]

What if I reversed it to be:

Setup2
Index Documents = ["cat", "bat", "monkey"]
Queries = ["hat", "funny"]

Is it guranneted that

X = Setup1.FuzzyQuery(Y)
Y = Setup2.FuzzyQuery(X)

For example if in Setup1

Query "cat" will result in ["hat"] 
Query "bat" will result in ["hat"]

Is it guranteed that in Setup2

Query "hat" will result in ["cat", bat"]

searched online and checked ElasticSearch documentaion but found nothing