DSE tightly links Solr collections and Cassandra column families.
DSE supports any number of column families, and hence, any number of Solr collections, even on a single node.
DSE/Solr is roughly equivalent to Solr Cloud - both support any number of collections.
Cassandra has partitions of its rows, while Solr has shards of its documents.
But under the hood, DSE/Solr uses Cassandra for managing the cluster, partitioning (sharding), replication, etc.
The stored values for a collection are kept in Cassandra in DSE, not in Solr. Solr/Lucene is used strictly to support search in the Solr/Lucene index. Once a document is found via the Lucene/Solr index, the fields/columns of the documents are fetched (under the hood) from Cassandra, given the key for the document.
DSE/Solr does still use some of the SolrCloud technology, but not for the actual partitioning and replication, which are handled strictly by Cassandra or DSE/Sor itself.
As with Solr Cloud, DSE/Solr has a single instance of a Solr server per node, and a single Solr core for the portion of each collection that is partitioned (sharded) on that node.
Solr and Cassandra replication are very different. With Solr, each replica is a copy of a shard for all of the collections. But with Cassandra, each Solr core includes the replicas for other partitions of that collection, up to the replication factor.
Strictly speaking, DSE/Solr does not support traditional Solr "multi-core", in which the user is manually managing individual cores. With DSE - and SolrCloud, the user manages entire collections, distributed across a cluster. Sure, under the hood, DSE USES multiple Solr cores per Solr server instance, but not in the strictly ad hoc sense of traditional, pre-SolrCloud multi-core support.
So, yes, DSE/Solr uses the Cassandra partition and replication strategy.
Yes, DSE/Solr automatically distributes portions of queries to other nodes in the cluster to retrieve the query results for the partition of the column family on that node, and then automatically aggregates the combined query results. The user can send a query to any node, as with SolrCloud.
Updates can be sent to any DSE/Solr node, similar to SolrCloud, except that DSE/Cassandra handles the data distribution to other nodes and for replication.
To be clear, collections can span nodes - in both SolrCloud and DSE, but a Solr core contains only a portion of the total documents/rows of the collection. Although, for an n-node cluster with a replication factor of n, indeed all documents of each collection/column family will be on all nodes of the cluster.
To be clear, a Solr core is, by definition, only on a single node. It is the collection that spans nodes, as with SolrCloud. Each Solr core will have its own Lucene index for each field in the collection. Lucene indexes are also, by definition, on a single node, and contain only the subset of the collection documents that are partitioned or replicated to that node.