The best way I've heard it described (I can take no credit) - consider memory your desk at work, where your current work is placed and worked on, storage is like your drawers or filing cabinet.
Now, people will often interchange the term (companies advertising products even do it). Bottom line, your device has 8, 16, 32, 64 or 128 GB of storage and 1, 2 or 3 GB of memory. The storage is what is freed up when you clear cache, delete data, etc.