Heal is the mechanism through which most units can regain health.
Most healing effects are subject to crit and crit damage.
Most healers heal units based on their own maximum health, and modified by the skill, possible souls, their crit, and crit damage, and status effects.
Healing may be possible outside of the healer's own turn, such as Sakura, Ebisu, and Hiyoribo.
Heal over time can also crit.
Healing Based on Other Stats
Sometimes the healing to the unit is not reliant on the healer's health, but the target's health. Other units have skills that heal themselves only and so are only based on their own attributes. Hotarugusa is particular in that she heals according to the attack value of her attacker, compared to the damage-based healing of Hiyoribo. Meanwhile, neither Umibozu nor Hotarugusa have HP Stealing skills.
A soul like Holy Flame also recovers percentage-based health.
Since various shikigami in the game have various skillsets, they may be limited to the kinds of units that can be healed. For example, some healers are not capable of healing summoned creatures.
Units with a heal-based status effect maybe also heal less or basically not heal at all (a 100% heal block only allows healing of 1 HP).
HP Steal & Recover
HP Stealing or Recovery is usually dependent on the damage dealt, which is itself based on factors such as crit, crit damage, status effects, etc.
However, they are different from healing or restoring and cannot crit, are unaffected by reduced healing effects and do not trigger effects related to healing.
Units are revived where they were on the move bar, so the move bar does not reset for them. This is the same across all skills such as Jikikaeru, Oguna, Momo, and Hiyoribo.
Note that for Kagura's offering skill, revival happens on the spot.
Revival mechanisms can interfere or be interfered by other skills, depending on the particular case and the activation order. They may even override afterkill effects. Hangan's skill is special in that it deals extra damage to revived targets, no marking required.