Each Node can have any number of children (unlike a Binary Tree). But all Nodes in a Trie will have the same maximum number of Nodes, corresponding to the size of the alphabet of characters.
Unlike a Binary Search Tree, the position of a Node in a Trie indicates the Node's position in the sequence, not a relative comparison to the parent. Each sibling of Node n has the same chain of ancestors (prefix) and a distinct value relative to it's siblings.
Some Nodes correspond to just parts of words (e.g. "swe"). Some Nodes correspond to complete words (e.g. "sweet"). A given Node can be both (e.g. "sweet", which is both a prefix of "sweetest" and the complete word "sweet"). Each Node has a flag that indicates whether or not the Node corresponds to a complete word.
Tries are also called Prefix Trees.
Suffix Trees are a special kind of Trie.