Normally, "memory" refers to primary, semiconductor based storage, but this is a very blurred distinction.
Each type of storage is suited for different purposes, and most computers contain several types.
Primary storage contains data that is actively being used (for example, the programs currently being run and the data they are operating on). It is typically high-speed, relatively small, and is often (but not always) volatile. It is sometimes referred to as "Main Memory".
Secondary storage is where the computer stores information that is not necessarily in current use. It is typically slower and has larger capacity than primary storage. It is almost always non-volatile.