This is only a partial answer. The most it attempts is to illustrate how to approach this question: I would like a clear answer to the distinction between inference and deduction.
Answers may differ depending on the logicians one is quoting. One can expect all of these answers to be clear, that is, internally consistent from any particular logician, but not that all logicians will agree on any one definition.
Here is how the authors of forallx use inference: (page 8)
So: we are interested in whether or not a conclusion follows
from some premises. Don’t, though, say that the premises infer the
conclusion. Entailment is a relation between premises and conclusions; inference is something we do. (So if you want to mention inference when the conclusion follows from the premises, you
could say that one may infer the conclusion from the premises.)
For these authors there are subtle differences between entailment and inference.
They use deduction to describe "proof-theoretic" systems, such as "natural deduction", in contrast with semantic arguments using truth tables or interpretations: (page vi)
But entailment is not the only important
notion. We will also consider the relationship of being consistent, i.e., of not being mutually contradictory. These notions can
be defined semantically, using precise definitions of entailment
based on interpretations of the language—or proof-theoretically,
using formal systems of deduction.
One thing to note from this is reaching a usable definition of a term may require multiple concepts to keep track of, such as, entailment, consistency, mutually contradictory, semantic, interpretations, and formal system. A full understanding of inference and deduction may require understanding other terms as well.
To see how things might be done differently, Quine uses the two words in the following note: (page 88)
Frege was perhaps the first to distinguish clearly between axioms and the rules of inference whereby theorems are generated from the axioms. Once this distinction is drawn, a recursive characterization of the class of theorems is virtually at hand. But the highly explicit way of presenting formal deductive systems which is customary nowadays dates back only to Hilbert (1922) or Post (1921).
The important thing to observe besides any differences with the previous use of the words is that these terms not only have a definition but they also have a history. One way to acknowledge that history is to associate any definition with whomever is the source of that definition.
So, for a clear answer to the distinction between inference and deduction one needs to further specify which logician's definition of these terms one is interested in.
Because of the differences between logicians I don't have an answer to the final question: Is there any widely agreed upon difference between "deduction" and "inference"? If so, what is it? If not, in what ways might the terms differ?
I suggest, however, given the above, that one doubt any answer one might receive to such questions. Any answer to the differences between these terms should also be associated with the logician providing the description of those differences, because the chief way the terms differ is due to their different sources, that is, the different logicians providing those definitions.
P. D. Magnus, Tim Button with additions by J. Robert Loftis remixed and revised by Aaron Thomas-Bolduc, Richard Zach, forallx Calgary Remix: An Introduction to Formal Logic, Winter 2018. http://forallx.openlogicproject.org/
W. V. O. Quine, (1981) Mathematical Logic, Harvard