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Are they the same? Empirical models, per Wikipedia, are

any kind of (computer) modelling based on empirical observations rather than on mathematically describable relationships of the system modelled.

But since data-driven models are also based on observations, what is the difference?

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They are the same thing, but it is important you understand differences in process between the statistics school of thought and the data mining mining school of thought. In data mining we impute and approximate relationships, where as some relationships are certain and have precise computations. Obviously, it is always better to compute something precisely than to approximate a relationship.

An example in finance: Bond prices have precise computations - they follow a certain relationship. The are simply discounted cashflows. Other types of securities might require inference because the absolute relationship is unknown, likely because either the cashflow or the interest rate is not known.

Empirical means based on evidence or observations. You are testing something. It might be possible to generate data per a simulation - this is common with genetic models - that is not observed in real life. In that instance, your data driven model would not be empirical.

em·pir·i·cal /əmˈpirik(ə)l/ | adjective | based on, concerned with, or verifiable by observation or experience rather > than theory or pure logic. "they provided considerable empirical evidence to support their argument"

Data mining versus statistics:

Normally what you try to do in statistics (as opposed to data science / data mining) is you come up with the definate mathematical model first, the you test it empirically. If the relationship is statistically significant, than it is thought to be a good model.

In data mining you seek out the inferred relationships first and have no manner of testing them.

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Just to add a bit of context to Michael's answer: empirical is a more general term which describes a scientific approach based on observations/experiences, as opposed to theory.

The empirical approach exists for a long time and can be used in many different contexts, including when the process is manual and the observations are not very formal (e.g. feelings in psychology).

Data-driven is a recent term which usually refers to Machine Learning (although not exclusively), i.e. using a formal set of observations in order to build a representation of a population of interest (usually through automated methods). So data-driven can be seen as a formal, usually automatic version of the empirical approach.

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