TL;DR: IMO, data-driven is a broader term, but it's a matter of definition.
Different people might have different understanding of the terms "Machine Learning" and "data-driven", so I'm slightly (pleasantly) surprised that this question hasn't been closed as "opinion based". Since it still stands, I'll offer my opinion.
Historically, Machine Learning evolved as an attempt to make machines "intelligent", by allowing them to learn from "experience" (i.e. data), often by mimicking how living beings learn. So it was necessarily "data-driven". In other words, ML $\subseteq$ DD.
However, some statisticians also consider statistical modelling to be "data-driven" (e.g. Efron & Hastie, "Computer age statistical inference", p. 264). If you agree with that and if you consider data-driven statistical methods to be distinct from Machine Learning, then, obviously, "data-driven" is a broader term: DD $\supset$ ML.
(Personally, I'd rather contrast "data-driven" to "domain knowledge-driven", "probability model-based", or simply "parametric", but still leading to the same result)
There is, of course, considerable disagreement about terminology. Some statisticians consider Machine Learning to be a subset of Statistics (and most machine learners would disagree). Some machine learners consider some traditionally statistical methods, like linear or logistic regression, to be "machine learning" methods (and most statisticians would disagree). If you side with the statisticians on this point, these models would be examples of data-driven models that are not machine learning.
P.S. I disagree with bogovicj's comment. ML always builds models, only in some cases these models are not made explicit to the users. But ML algorithms certainly make some internal representations of the "things" (e.g. classes) they have learned and these representations are, for all practical purposes, synonymous to "models".