A time series database is an abstraction where a timestamp [1] is the key in the first order tables. Often the abstraction is built on top of some well known database because getting all the bits to write and read from storage is a hard problem where existing solutions exist. For example, Kairosis built on Cassandra [2] and OpenTSDB uses Hbase. [3]. It's not the only way to do it, InfluxDB uses its own back end. [4]

[1] or a tuple of timestamp and some other values.

[2] https://kairosdb.github.io/

[3] http://opentsdb.net/

[4] https://www.influxdata.com/