I don't think there is a huge difference in the meaning of the two terms, although hedge is also used as a technical term for specific linguistic devices, whereas tentative is a more descriptive term for the style of writing. (See the Wikipedia article linked for categories of hedges with examples.)
Hedges and politeness
In a comment, Edwin Ashworth points out:
"Hedges can also be used to politely give commands and requests to others:
Could you please shut the window, Phil?
Wikipedia includes this, but omits it in its introductory overview."
In the linguistic sub-fields of applied linguistics and pragmatics, a
hedge is a word or phrase used in a sentence to express ambiguity, probability, caution, or indecisiveness about the remainder of the
sentence, rather than full accuracy, certainty, confidence, or
decisiveness. Wikipedia
Tentative language is particularly used in the writing of academic papers because the purpose of academic papers is questioning what is
true and why it is true. Tentative language puts forth ideas as ideas,
rather than offering ideas as definite answers. Sometimes tentative
language is called hedging or vague language. The writers of academic
papers use tentative language or hedging for several reasons:
They downplay their statements in order to reduce the risk of possible opposition, especially if their statements, arguments or
claims are new and need further verifications.
One could consider hedges as ways of being more precise in reporting results because academic writers may well wish to reduce the
strength of claims simply because stronger statements would be
justified by the data or evidence presented.
Sometimes they use hedging in order to appear humble rather than arrogant or all-knowing. B. Klimova; "Using Tentative Language in English" in Procedia, Vol. 116 (2014)
Hedging is thus not always a "politeness tool" and, as mentioned, is common in the sciences when authors wish to "reduce the strength of claims," as Klimova states. In any case, care must be taken not to overdo a hedge. This is a frequent problem when authors who are not fluent in English write for scientific journals, especially in the Conclusion section. Such stylistic problems (as well as grammatical errors) used to be corrected before publication, but for many journals those days are long gone. (My own past experience correcting English drafts of Italian scientific papers translated by the authors is that double and triple hedges don't seem to raise many flags: each hedge in the original gets faithfully translated.)
Examples:
As for the potential benefits of the treatment from data on patients
without ADs [autoimmune diseases], we may extrapolate that there
may be a possible effect on large number of patients who develop radiographic progression and reduction of symptomatic days,
but an additional benefit of the addition of Azithromycin (AZ) to
therapy is uncertain. T. Georgiev and K. Angelov; "Complexities of
diagnosis and management of COVID-19 in autoimmune diseases: Potential
benefits and detriments of immunosuppression" in World J Clin
Cases (2020)
These results suggest that AAS [anabolic-androgenic steroids]
could be a possible new risk factor for TAFLD [toxicant-associated fatty liver disease]. R. Schwingel et al.;
"Anabolic-androgenic steroids: a possible new risk factor of
toxicant-associated fatty liver disease" in Liver International
(2010)
