Unless you literally put your cash under a mattress, savings _is_ investment (e.g. bank deposit being lent out, money market funds invested in corporate paper,

Unless you literally put your cash under a mattress, savings _is_ investment (e.g. bank deposit being lent out, money market funds invested in corporate paper, Treasury holdings, etc.). The savings is always "held" (invested) in some form of an asset, not cash under the mattress.