A trie itself is a generic term for a data structure that stores keys implicitly as a path. If you google tries, you will see that there are multiple different implementations for a searching data structure where the keys are stored in this way, and thus, there will be different space complexities for each. One that comes to mind from my personal studies are the R-Way Trie, which uses an array of size R (if your keys can be any ASCII character, R would be 256) to store references to additional characters in the key. Each node in this structure thus has to allocate memory for an array of size R, so in terms of space complexity, this trie is O(RN) where N is the number of keys.
Another trie I studied is the DeLabrandais trie, which uses linked lists instead of arrays to store references to additional characters in the key. From a memory perspective, this trie actually is better because it allocates memory as needed for each additional character as opposed to allocating one giant chunk that will probably be partially empty (assuming a non-equal distribution of characters in keys stored). This structure however will take longer to search for a key as you lose the direct access of the reference arrays and might now have to traverse a linked list. Asymptotically, the DLB trie (I think, but might be wrong) is still O(RN), but its memory consumption is practically better in most cases because of the non-equal distribution of characters in keys that I mentioned previously.