1. A system, comprising: one or more computing devices configured to: determine, by one or more control components of a multi-tenant stream management service, wherein the one or more control components are assigned to a particular data stream comprising a plurality of data records generated by one or more data producers, a respective set of nodes of (a) a record ingestion subsystem, (b) a record storage subsystem, and (c) a record retrieval subsystem, wherein each subsystem of the record ingestion subsystem, the record storage subsystem, and the record retrieval subsystem comprises one or more nodes dynamically configurable by the one or more control components based on one or more policies including a partitioning policy; receive data records submitted via one or more programmatic record submission interfaces implemented at the record ingestion subsystem, wherein the one or more programmatic record submission interfaces include a first submission interface supporting in-line submission of data records and a second submission interface enabling submission of data records by reference to network addresses at which data is stored; provide contents of data records in response to data record retrieval requests received via one or more programmatic record retrieval interfaces implemented at the record retrieval subsystem, wherein the one or more programmatic record retrieval interfaces include a first retrieval interface enabling a non-sequential access pattern and a second retrieval interface enabling a sequential access pattern, and wherein a billing rate associated with a use of the first retrieval interface differs from a billing rate associated with a use of the second retrieval interface; generate a client billing amount associated with the particular data stream based at least in part on respective usage count metrics of the plurality of record retrieval interfaces and the plurality of record submission interfaces.