HSEARCH-4142 Apply suggestions from code review

Co-authored-by: Yoann Rodière <yoann@hibernate.org>

documentation/src/main/asciidoc/reference/search-dsl-projection.asciidoc

@@ -87,10 +87,12 @@ include::{sourcedir}/org/hibernate/search/documentation/search/projection/Projec
 NOTE: The entity does not get loaded as part of the projection.
 If you want the actual entity instance, use the <<search-dsl-projection-entity,`entity` projection>>
 
-== `id`: return ids to matched entities
+== `id`: return identifiers of matched entities 
 
-The `id` projection returns the id to the matched entity.
-The API allows to express the expected entity type of the returning ids.
+The `identifier` projection returns the identifier of the matched entity.
+NOTE: If the provided identifier type does not match the type of identifiers for targeted entity types,
+an exception will be thrown.
+See also <<search-dsl-projected-value-type>>.
 
 .Returning ids to matched entities, providing the identity type.
 ====
@@ -99,6 +101,7 @@ The API allows to express the expected entity type of the returning ids.
 include::{sourcedir}/org/hibernate/search/documentation/search/projection/ProjectionDslIT.java[tags=id-int]
 ----
 ====
+You can omit the "identifier type" argument, but then you will get projections of type `Object`:
 
 .Returning ids to matched entities, without providing the identity type.
 ====
@@ -108,9 +111,6 @@ include::{sourcedir}/org/hibernate/search/documentation/search/projection/Projec
 ----
 ====
 
-NOTE: If the provided identity type does not match the current returned ids,
-an exception will be thrown.
-
 [[search-dsl-projection-entity]]
 == `entity`: return matched entities
 

engine/src/main/java/org/hibernate/search/engine/search/projection/dsl/SearchProjectionFactory.java

@@ -47,11 +47,6 @@ public interface SearchProjectionFactory<R, E> {
 	/**
 	 * Project to the identifier of the referenced entity,
 	 * i.e. the value of the property marked as {@code @DocumentId}.
-	 * <p>
-	 * The actual type of the reference depends on the mapper used to create the query:
-	 * the ORM mapper will return a the identifier, for example.
-	 * <p>
-	 * Using this method we do not provide any assumption about the type of the identifier.
 	 *
 	 * @return A DSL step where the "id" projection can be defined in more details.
 	 */
@@ -62,13 +57,8 @@ default IdProjectionOptionsStep<?, Object> id() {
 	/**
 	 * Project to the identifier of the referenced entity,
 	 * i.e. the value of the property marked as {@code @DocumentId}.
-	 * <p>
-	 * The actual type of the reference depends on the mapper used to create the query:
-	 * the ORM mapper will return a the identifier, for example.
-	 * <p>
-	 * Using this method we assume that the type of the identifier is a subtype of {@code identifierType}.
 	 *
-	 * @param <I> The resulting type of the identifier
+	 * @param <I> The expected type of the identifier
 	 * @param identifierType The expected type of the identifier
 	 * @return A DSL step where the "id" projection can be defined in more details.
 	 * @throws SearchException if the identifier type doesn't match