Sure. But that doesn't solve the problem. As with words in general, meanings change and are different in different fields. And there are different formal definitions. For instance, the Oxford Dictionary of Statistics ed. by Upton and Cook, defines "inference" as
The process of deducing properties of the underlying distribution by
analysis of data.
It does not have an entry for "prediction" but, for "prediction model" it has
In a medical context, a model used to predict an outcome or the
probability of an outcome....
That seems to fit how the term is used in some other fields, as well.
Britannica has a similar definition for "inference":
inference, in statistics, the process of drawing conclusions about a
parameter one is seeking to measure or estimate.
And, of course, there are definitions right here on CrossValidated, although they may not meet your idea of "formal".
For myself, I would say that prediction is about some future, possibly hypothetical, state of things, while inference is about a population from which you have a sample. If I take a sample mean and then take confidence intervals and so on, I am not necessarily predicting anything, but I am inferring from the sample to a population.
But you may not agree with my (informal) definition.
EDIT: After reading Richard's comment, I agree with his distinctions.