It seems that there are two terms that could be broadly translated as "gratitude", which each express different aspects of the concept. הכרת הטוב denotes recognition, while הודאה has strong echoes of active admission. I know that both are brought up in the literature, even co-occurring in רש"י's comment on the birth and naming of יהודה. Does anyone explicitly contrast the two concepts of gratitude?
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Hakaras haTov, although in a simple sense is an awareness like Yahu said, is a responsibility that manifests itself in an action or inaction, though not necessarily of hodaah.
An example off the top of my head is the Ramban on why Ammon was kicked out of the Kahal more than other nations who didn't take nourishment to the Bnei Yisrael. He answers that since Lot was saved by Avraham, Ammon had a responsibility to do good to the B'nei Yisrael, and they did the opposite.
Bringing nourishment is not "hodaah", any nation would have done so, and they did (Edom as well as Moav). But Hakaras haTov creates a higher responsibility of reciprocity toward those who benefited you. What actions or inactions will one take in recognition of being a beneficiary?
Hodaah is a verbal or physical acknowlegement of the benifit (like saying thank you). You can give hodaah to someone with good intentions even if you didn't actually have a benefit. In that case, you don't have a responsibility toward the benefactor, but you can be grateful for his intentions.
Rabbi Frand addresses the definition of each of these words in a different Dvar Torah.
On Parshat Shoftim he addresses the meaning of the words HaKaras HaTov which is generally translated as gratitude. He explains why they Talmud tells so many stories about Amoraim recusing themselves as viable judges just because they had received a favor from one of the litigants. "The major lesson that this passage of Talmud teaches is the concept of Hakaras HaTov [gratitude]. This Gemara teaches us how indebted each of these Amoraim felt to anyone who did them even the slightest favor." He seems to be indicating here that HaKaras HaTov is the indebtedness we feel and should show towards another. He explains that even acts that we have come to expect from another, like a spouse or an employee, should still induce a feeling of HaKaras HaTov.
On Parshat Tzav he addresses the meaning of Hoda'ah defining the word as both 'thanks' and 'admitting', giving credit for these definitions to Rav Hutner. We must admit we needed someone before we can thank them.
So if we take both his meanings and put them together it appears that we should have HaKaras HaTov toward everyone who helps us and serves us, whether we needed it or not and Hoda'ah is thanking someone for something we could not have done on our own.
Strict translation of Hakoras Hatov is gratitude / Hoda'a is praise.
When a person makes a Seudas Hoda'a for a Neis that happened to him he is praising Hashem for the Neis. Praising includes a proclamation of thanks. When a person appreciates what someone did to help him that is Hakoras HaTov. It does not necessitate a proclamation and can be done quietly in appreciation.