I think that your understanding of suffix links and failure links is incorrect. In both cases, a suffix/failure link is a pointer from one node in the trie/suffix tree to another node in the trie/suffix tree with the following property: if the original node represents the string x, then the string y encoded by the node pointed at by the suffix/failure link is the node for which y is the longest possible suffix of the string x.
The main difference between the two algorithms is what the algorithms produce rather than what the suffix/failure links mean. Aho-Corasick produces a trie annotated with extra transition information that makes it possible to find all instances of a collection of strings as rapidly as possible. The failure links produced are used both in the construction of the algorithm and in the pattern-matching step. Ukkonen's algorithm produces a suffix tree, using the suffix links only during construction and not during most queries on the tree.
Hope this helps!