SELECT – Return a table of results.
CONSTRUCT – Return an RDF graph, based on a template in the query.
DESCRIBE – Return an RDF graph, based on what the query processor is configured to return.
ASK – Ask a boolean query.
The SELECT form directly returns a table of solutions as a result set, while DESCRIBE and CONSTRUCT use the outcome of matching to build RDF graphs.

CONSTRUCT
CONSTRUCT builds an RDF based on a graph template.  The graph template can have variables which are bound by a WHERE clause.  The effect is to calculate the graph fragment, given the template, for each solution from the WHERE clause, after taking into account any solution modifiers. The graph fragments, one per solution, are merged into a single RDF graph which is the result.

Any blank nodes explicitly mentioned in the graph template are created afresh for each time the template is used for a solution.

DESCRIBE
The CONSTRUCT form, takes an application template for the graph results. The DESCRIBE form also creates a graph but the form of that graph is provided the query processor, not the application. For each URI found, or explicitly mentioned in the DESCRIBE clause, the query processor should provide a useful fragment of RDF, such as all the known details of a book. ARQ allows domain-specific description handlers to be written.

ASK
The ASK result form returns a boolean, true of the pattern matched otherwise false.