Healing, Lifesteal, and Regeneration

I've started building my own item builds based on my play style. It's been a long journey to that point, but (since watching the Season 3 Pro League) I've been recently starting to understand how certain gods work with certain items.

So, my question has to do with the concept of Healing versus Lifesteal versus Regeneration: Is there a difference when it comes to items?

Let me explain my question -

I was reviewing Gauntlet of Thebes. I know that this is a 'selfish' heal (unlike items like Rod of Asclepius and Lotus Crown) and that it only affects me as the one being healed or, as my examples will question, self-healing.

There are several gods that I have played that can 'self-medicate', but their descriptions are slightly different.

• Tyr - Power Cleave - This makes sence: At max, it heals 105, so plus 20% equals 126.
• Bellona - Scourge - This makes sence: At max, it heals 50, so plus 20% equals 60.
  
• Ao Kuang - King of the Eastern Seas - Question: Does this mean whatever the healing was and then 20%? So, if my maximum health was 2,000 (and this ability was maxed), I would heal 600 health (30%) and then another 120 health (20%)?
• Zhong Kui - Exorcism - Question: Does this mean whatever the healing was and then 20% (up to the max)? Or can this item push it past the max - Let's say I max healed at 240 per demon. Would Gauntlet of Thebes allow another 48 health (20%) even though it is past the max?
  
• Vamana - Colossal Fury - Question: The description reads that he 'regenerates' 5% of his health? Does this count as healing such that Gauntlet of Thebes would have an effect? I don't know if regeneration counts as healing.
  
• Freya - Brisingamen's Blessing - Question: This pertains, actually, to all lifesteal. Does lifesteal count as healing? Does Freya or any item that allows for lifesteal (like Asi) add another 20% healing from Gauntlet of Thebes?

I look forward to hearing from you. Thanks! :)

I didn't test all of these scenario, but my guess would be YES to all of these.

It increases all healing, therefore meaning
- Healing from an ally (ex: Love Birds)
- Self healing ( Power Cleave)
- Health regeneration ( Smouldering Rage / Stone of Gaia)
- Lifesteal ( Asi / Pythagorem's Piece)

As for your "maximum" stat, you are not interpreting it in the right way.
Many abilities have a maximum values. These are used give to help you calculate the theorical total of damage/healing)
Examples:
Death Gaze is the total damage done if every tick hits the target.
Love Birds is the total damage and healing done once all ticks are done.
Power Cleave is the total healing received from the 3 targets maximum
etc.

So, Exorcism, at max rank, heals for 80hp (+20% magical power) per target, up to 3 targets.
So, if you hit 3 targets, you get healed for 240hp (+60% magical power)
But if you hit more than 3 targets, you only get the benefit for only 3 of them.
That's why they say (up to 3) in the description.
Therefore, the maximum "basic" healing is 240xp (+60% magical power).

After, this amount can be affected by
- Healing bonus ( Gauntlet of Thebes / Rod of Asclepius)
- Anti-healing ( Divine Ruin / Curse / Ring of Spears / Moonflower Dance, and many others)

I tested these situations out of curiosity, and here's what I got:

Tyr's Power Cleave - works, it's simply healing

Bellona's Scourge - works, as with Tyr

Vamana's Colossal Fury - works, regeneration counts as healing regarding Gauntlet of Thebes (that's why it's good on Hercules)

Zhong Kui's Exorcism - works; the ability's suggested "maximum amount" is simply calculated at the maximum count of demons that can multiply its healing- in this case it's 3 of them (hence +60% of magical power; +20% for each)- but it can of course be further multiplied by the Gauntlet's passive

Ao Kuang's King of the Eastern Seas - works, increases amount healed by 20% of that amount (so Your example is true: 600 + 120)

Freya's Brisingamen's Blessing - works, and with lifesteal in general; it multiplies the total amount healed by lifesteal- for example an auto-attack heals for 10, with Gauntlet- 12

I also tested other sources:

Meditation - works
Healing Potion - works
Stone of Gaia's passive - works

So, in general, Gauntlet of Thebes' passive works with every (I think) mechanic that restores health, excluding the basic HP5 regeneration (these small amounts regenerated passively over time)- and it's taken into account after the effect; best way to imagine it is to take the green amount of +health that shows up on the screen and multiply it by 120%.

EDIT:
As a bonus information; if multiple healing-altering effects are taken into account, for example Gauntlet of Thebes and Rod of Asclepius- their increase will be calculated off the basic amount; for example a heal heals for 100, with Gauntlet it would be 120, and with Rod 140, not 144 that could be expected (100 * 120% * 120%)- also because of that, in theory one would be able to heal with 20% efficiency inside Odin's Ring of Spears with Rod of Asclepius.

The healing part boost has been explained. Lifesteal stacks the same way (so an item of 20% lifesteal + 30% lifesteal should be 50% lifesteal.)

However the regen and lifesteal are pretty weak compared to the healing. especcially when in battle as healing provides you in most cases with a faster pool of health.
The others are weaker during a fight as they don't provide as big of an amount as most heals.

This is why the regen tree is pretty bad atm they do provide HP but the stats are a bit worthless as you can't use them really well during a fight. only after a fight.
For lifesteal kinda counts the same but the items provide better stats and the users have pretty high damage making the total heal they get bigger.

That is a fact, if you get any +healing bonus, you can heal in Odin Ring of Spears or while affected by Lord of the Afterlife.
Rod of Asclepius is mainly used to partly counter the anti-healing items/effects.