Likert: Fisher's exact OR Kruskal-Wallis?


I've got a survey with 50 responses, and want to test for difference between three subgroups, and strength of association. I'm not happy to treat data as continuous.

But I'm not sure whether I should use Kruskal-Wallis to compare rating scores between groups, or Fisher's Exact Test, on the assumption that ordinal data is just a specific version of nominal data.

What's worse, the Fisher's test gave me statistically significant differences, while the K-W didn't. How can that be, and is it meaningful?