Hydrogen peroxide, developer or activator is the 'white' stuff you use to mix and activate your hair dye to turn it into hair dye prior to slapping it on your hair :D
It is H202, and it is a oxidizing agent that you use to mix with an oxidative agent such as Hair Dye. It supplies the needed oxygen the dye needs to pretty much 'activate' it. PH levels usually range between 2.5 to 4.5 When mixed together with the dye and applied to the hair, the activator reacts and 'opens' up the hair cuticles to allow the hair dye to penetrate the hair shaft. The higher the level of the developer, the higher the your color will 'lift'
You mentioned different names and forms?
Most places/people call Hydrogen Peroxide 'developer' or 'activator' as described above.
It comes in different forms, such as your regular basic liquid cream form (white liquid), gel (clear liquid. I personally dont like using gel as it tends to be runny) and sometimes even a heavier cream version which is best used for when bleaching your brows :D as its a thicker consistency allowing no drips or drops at all!
Levels and their usages:
H202 comes in different levels, the most basic levels you'll be able to access through your local beauty supply sheps are vol. 10-40. and Yes, they DO make developers as high as vol. 50 and 60 BUT are never advisable to be used at all! :O so dont worry about those, unless you are a licensed cosmetologist, you wouldnt be able to access anything higher than 40. And most places wont even sell you vol. 40)
Vol. 10 - Used to enhance ones own natural hair color, it doesnt 'lift' your hair color at all but it definitely works for depositing color and using it to enhance your natural shade. This developer gives the least amount of damage or NO damage at all considering its not even strong enough to open up the hair shaft.
I always suggest this to anyone who has pre-lightened hair and wants to go darker.
ie: When a friend went from black to blonde (and we all know when asians bleach their hair, is usually pretty yellow), she wanted to go 3-4 shades darker but still remain in the blonde range. So we used vol. 10 + the dye. Mixed them accordingly and reapplied to her hair.
Vol. 20 - most standard of the developers, this is the one most commonly used in boxed dyes (usually the ones that comes in the boxes are alittle bit more dilluted), this is also the developer used for full gray coverage. This would lift your hair 2 shades.
its strong enough to open up the hair cuticles and deposit the dye just enough but not too strong that it'd completely open up the hair shaft.
Vol. 30 - Use this for alittle bit more of a KICK to your hair lifting, this would lift you up atleast 3 volumes and is most commonly used with 'Hi Lift Colors' Most commonly adviced when using L'oriel high lift colors, per box instruction
Vol. 40 - Highest max lift in 1 step. This would lift you a nice 4-5 shades in one step.
I highly advice this for anyone going Blonde :B since it def helps lift you up a good 4-5 shades.
I wont go into detail in regard to 'how do I lift my hair to blonde blablabla, atleast not on this post. :D I'll go into it much more detailed in a different post. This is just a basic break down on Developers and what they do and whatnot.
What are the 'hair levels' you're talking about?
Your hair comes in 10 different 'shade levels'. Most Asians are either a level 1 or 2. Which is Black or Dark Brown. When 'lifting' your hair, you can use this chart as a guide to see how 'high' you wanna go:
Photo provided from Clairolpro.com
Will using a higher level above 10 be damaging to my hair?
Yes. The higher the level you're using, the stronger the chemical is, harsher it is on your hair, seeing as the higher the level the more it opens up your hair shaft.
As seen in the photo below, provided by hairfinder.com (found via google images)
the higher the developer, the more it 'raises' or opens up the hair to allow maximum porosity. The stronger the developer, the more it blasts or raises the hair cuticle which in turn, does damage your hair more and more making your hair feel more dry and course since you're taking out all that moisture and nourishment. So I always suggest babying your hair with masks and deep conditioners to try and close the cuticle and restore moisture.
When looking for a conditioner or hair masks, try to find ones that has 'Keratin Protein' in it.
keratin protein is basically the compound your hair is made out of and is very healthy for your hair to try and get as much of that keratin protein back into your hair.