Yes, that is true. The Smrti makes up the Dharmasastras.

But this classification as you have said earlier is contentious. To better understand this, we must know what the Dharmasastras are.

The 6th anga of the Veda is the Kalpa which deals with the methods to be followed for rituals. Obviously there are several injunctions on what to do and what not to do. These are given in the form of the Kalpa Sutras which themselves are several. A sutra is a terse utterance, a very pithy statement.

The Dharmasastras were later expounded to explain these sutras. Thus, they became elaborate treatises that deal with what to do and what not to do in order to live a life as ordained by the Shruti. This gave rise to traditions to be followed or what we also call Sastras. This is Smriti.

In that case, why should we include Itihasa-Puraanadi as part of Smriti?

To understand this, we must look at the definition of the Smriti itself.

Samskara janyam jnanam Smrtih - Knowledge born out of recollection of doing is called Smriti

We have done something previously and when we recollect that, we call it memory. This is Smriti. Itihasa and Purana are tales of people who have followed this Dharma, as expounded by the Shruti. It is actually a recounting of their samskaras. Therefore, going by the previous definition of Smriti, this also comes under the same category of Smriti.