I recently read a book that says that “grave” sin is not “mortal” sin. Thus the author says that missing Mass is a grave sin, but it is not a mortal sin. Is this so?

No, grave and mortal mean the same thing in Catholic moral teaching. Hence, missing Mass without a serious reason is a mortal sin (cf Catechism No. 2181).
 
It is true today many moral textbooks and Church documents use the word “grave” more often than “mortal.” There are likely pastoral reasons behind this. For it was a growing tendency for many poorly catechized people to think “mortal” sin referred only to killing someone. So, there came the tendency to use the word “grave,” meaning “weighty or very serious sin” to refer to mortal sin. But, as you point out, this has led to other pastoral problems, wherein people do not often understand that grave and mortal mean the same thing.
 
Pope John Paul II found it necessary in 1984 to clarify that grave and mortal mean the same thing. He wrote: In the Church's doctrine and pastoral action, grave sin is in practice identified with mortal sin….There is no middle way between life and death. (Reconciliation and Penance # 17)