Your question is very interesting because it allows to understand a concept quite important for Romans. First of all I think that your question comes from the quite confusing lemma of the L&S ; for tis kind of research I would recommend the Thesaurus Linguae Latinae or, if the word is not in it yet, the Forcellini's Lexicon Totius Latinitatis. So my answer is based on this two instruments.
First of all, a little bit of etymology : as it said in the Dictionnaire Etymologique de la langue latine by Ernout and Meillet page 281-282, gratia cames from the adjective gratus who has some connections with an old indo-european which concerns the religious field. According to them (p. 282), the first meaning of this word is:
1° abstract : gratitude Cic. Inv. 2, 66 gratia est in qua amicitiarum et officiarum alterius memoria et remunerandi voluntas continetur. From this meaning it becomes : "action through wich gratitude is gained" whence favour.
2° : beauty, grace. This is the translation of the greek χάρις, and the use of χάριν matches with the latin gratia (ablative case).
Let's do this with favor p. 220-221 : this word cames from the verb faveo who means to favour. Its meaning is indeed favour or applause. But, the first use of this word is in Cic, Sest. 115 qui rumore et, ut ipsi loquontur, favore populi tenetur et ducitur.
So, we can comfortably see that, according to their etymology, the use of these two words is not always exchangeable : one cannot use gratia instead of favor in the second quote from Cic, Sest 115, It would make no sense.
Now, their use according the Thesaurus.
First for gratia.
PARS PRIMA: -a generatim.6.2.2205.80
A active: de oblatione favoris:
1 per homines in universum: a ultro facta: p. 2206, 47.
b in retributione beneficii: p. 2208, 37. c meton. de ipsa
re oblata: p. 2209, 1. d de favore mutuo: p. 2209, 18.
2 de favore inique iudicantium: p. 2209, 47.
B passive: de perceptione vel usu favoris: p. 2210, 13.
1 de statu (condicione) hominum: a generatim:
p. 2210, 17. b in re publica: p. 2211, 10. c accedunt ap-
6.2.2206.5posita usitatiora: p. 2212, 35.
2 de qualitate rerum: p. 2212, 65. a corporalium (α in
hominibus. β in reliqua rerum natura [p. 2213, 36]).
b incorporalium: p. 2214, 37 (α in arte dicendi. β in vita
et moribus [p. 2215, 46]).
6.2.2206.10 C iuncturae:
1 verbales sec. casus: p. 2216, 63.
2 nominales: p. 2221, 63. a gen. -ae pendet ex substt. b ex
subst. -a pendet praep. c. casu: p. 2221, 77. c epithetorum
collectio: p. 2222, 1. syn., opp. (p. 2223, 27). 6.2.2206.15
A loci extra iuncturas: p. 2223, 64. B iuncturae verbales
sec. casus: p. 2224, 12.
And the same for favor
generatim i. q. studium, benevolentia, probatio, inclinatio
sim. (rarius de inferioribus vel subiectis) ; II metonymice i. q. actio, qua favor ostenditur: A i. q.
6.1.386.40plausus, acclamatio, assensus quilibet voce plerumque (cf. Liv. 23,
46, 2 clamorem -is indicem) vel sonitu manuum nutu.
So, relying on the difference of dimensions of the two lemmata, we can easily see that gratia has a more important semantic field than favor wich has been used later and for a more specific semantic field.
So an answer could be this : yes, one among the meanings of gratia is the same of the first one of favor and they are in this case synonyms. But, even in this case, the word gratia is older and is perceived as more elevated than favor which is more an 'imperial' word.
Hoping that my answer is what you expected.
I apologize for my English.