What is the default edit distance for query_string

Hi,
I wonder about the default edit distance of query_string

For a document containing quick, the following query

 {
   "query": {
     "query_string": {
       "query": "quakc~2"
     }
   }
 }

can return the document. But the following query won't:

 {
  "query": {
     "query_string": {
       "query": "quakc~"
     }
   }
 }

But according to the documentation https://www.elastic.co/guide/en/elasticsearch/reference/current/query-dsl-query-string-query.html, if omit the number after tilde ~, the default edit distance is 2, the above two queries should have the same search result. Am I misunderstanding the documentation?

Thanks!

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