Yes and no. An iCloud ID is an Apple ID, but an Apple ID is not necessarily also an iCloud ID.
(If that's confusing, think: All elephants are gray. Not all gray things are elephants.
If you want to share purchases, you'd be much better off using Family Sharing. Any content purchased by any individual in the family is the property of the individual purchaser, but can be shared with anyone else in the family.
You could, alternately, use one Apple ID for purchases, and create new iCloud accounts for each of you, or use one for purchases and iCloud for one of you and the other just for iCloud for the other one.
The first option is the most desirable and easiest to manage.