I see them as two different things so think you could have two
Definitions on both come from First San Francisco Partners
Information Management is an organizational program that manages
the people, processes and technology that provide control over the
structure, processing, delivery and usage of information required
for management and business intelligence purposes.
Information, as we know it today, includes both electronic and
physical information. The organizational structure must be capable
of managing this information throughout its life cycle —
regardless of source or format (data, paper documents, electronic
documents, audio, video, etc.) for delivery through multiple
channels that may include mobile phones and online.
Data Management is a subset of Information Management. It
comprises all disciplines related to managing data as a valuable,
organizational resource. Specifically, it’s the process of
creating, obtaining, transforming, sharing, protecting, documenting
and preserving data.