There are two queries,one is created by QueryParser:
QueryParser parser = new QueryParser(field, analyzer);
Query query1 = parser.parse(\"Lucene\");
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The QueryParser parses the string and constructs a BooleanQuery (afaik) consisting of BooleanClauses and analyzes the terms along the way.
The TermQuery does NOT do analysis, and takes the term as-is. This is the main difference.
So the query1 and query2 might me equivalent (in a sense, that they provide the same search results) if the field is the same, and the QueryParser's analyzer is not changing the term.