The Bard's Tale IV offers a variety of saving methods. You can save anywhere (except combat) using the "save" feature found in the Options menu. In-game, The Bard's Tale IV uses save checkpoints (designated in game as "Luck Stones") and also saves when you exit the game from the Pause Menu.
If you use a Luck Stone, you will regain all your party's health back, and the game will be saved. You cannot re-save at the same Luck Stone repeatedly. Exiting from the Pause Menu will save the game, but will not restore your health.