Anaerobic = total absence of free oxygen (O2) or bound oxygen (NO2, NO3)

Anoxic = absence of free oxygen, but presence of bound oxygen.

Anoxic is a description of the environment - without oxygen. Mostly microbes live here, and oxygen is actually toxic to most of them. Hydrothermal vents is an example of an anoxic environment.

Anaerobic describes a condition of cellular respiration that is undergone in the absence of oxygen. Organisms in anoxic environments generally do not undergo this type of respiration, since they have evolved completely different methods for such. Some organisms are obligate anaerobes, meaning they can not use oxygen. Some are obligate aerobes, meaning they must have oxygen to survive. There are also facultative aerobes that use oxygen when it is available. Humans undergo anaerobic metabolism when we have exhausted our immediate oxygen supply, such as during levels of high intensity exercise.

:)

Anaerobic = total absence of free oxygen (O2) or bound oxygen (NO2, NO3)

Anoxic = absence of free oxygen, but presence of bound oxygen.

Anoxic condition for eg.,Ground water that has no dissolved oxygen or a very low concentration of dissolved oxygen (that is, less than 0.5 milligrams per liter)."

Anaerobic condition: for eg: complete absence of oxygen

I agree with Mr/Mrs Sudhir.

Oxic and anoxic are used to describe the conditions, for example, oxic soil, anoxic condition. Aerobic and anaerobic are used to describe the processes, for example, aerobic biodegradation, anaerobic metabolism.

Yes, Zhijiang Lu . Anaerobic and aerobic are referred to describe the processes that O2 is final electron acceptor or not. but oxic and anoxic are used to describe the presence of O2 at all.

anoxic environment have only bound oxygen but anaerobic environment do not have any type of oxygen neither bound nor free

"Anoxia" (adjective: "anoxic") refers to the condition of an environment where there is no molecular oxygen (O2).

"Anaerobe" (adjective: "anaerobic") refers to the condition of an organism which is able to thrive without molecular oxygen (O2).

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It seems that there may be a confusion stemming from the ambiguity of the term "oxygen", which can refers both to the oxygen atom (O) and to the molecular oxygen (O2).

First, there is virtually no place on Earth with no oxygen atom (O), since water is made up of H2O, air contains 21% (by volume) of O2 (plus minor ammounts of CO2 and water vapor), and the crust contains 46.6% (by weight) of oxygen atom (O). Thus, I think it can be misleading to say that there are environments without any type of oxygen (neither bound or free) on Earth.

Second, terrestrial life is impossible without the oxygen atom (O), since it depends on water (H2O) and all four major classes of biomolecules have the oxygen atom (O) in their chemical composition (nucleic acids, carbohydrates, proteins, and lipids).

In contrast, there are many terrestrial enviroments depleted of molecular oxygen (O2), and there are many organisms that can thrive without molecular oxygen (O2). These organisms are called anaerobes, and the etymology of this word reveals its biological origins: from the French word "anaérobie", coined by Pasteur in "Études sur la bière" (1863):

"On pourrait partager les êtres vivants en deux classes: les aérobies, c'est-à-dire ceux qui ne peuvent vivre sans air, et les anaérobies, qui, à la rigueur et pour un temps, peuvent s'en passer..."

Today, the adjective "anaerobic" is also used to the metabolic processes carried out by anaerobes, such as anaerobic respiration (in which the final electron acceptor is different from O2).

Therefore, one may say that anaerobes are able to carry out anaerobic respiration (or fermentation) under anoxic conditions.

http://www.cnrtl.fr/etymologie/ana%C3%A9robie

http://www.etymonline.com/index.php?term=anoxic

All wrong for anaerobic. The major difference of anaerobic conditions from anoxic conditions is that, on the top of absence of oxygen, the negative redox potential is playing the major role, necessary for growth of obligate anaerobes, mostly 3 groups of secondary anaerobes - SRP, acetogens and methanogens, but also some fermenters as well. The reason is that they produces enzymes and e-carriers with low-potential reduced cofactors which are inactivated irreversibly at high red-ox potential.

Wow!

I think the answer by Vinicius Waldow summarizes it better than anything I have read so far. That's what I leaned in Bernhard Schink's Lab. Thanks for that comment!

I agree with Mr. Vinicius Waldow & Mr. Medi Begloui . 

In my point of view, the classification of the anoxic and anaerobic condition is based on the presence of different electron acceptors. Under the anoxic condition, nitrate, nitrite or sulfate could be used as an electron acceptor, while organic carbon will be used as electron acceptor under anaerobic condition. 

aerobic conditions - DO > 2 ppm

micro aerophilic - DO : 0 - 2 ppm

anaerobic - DO : 0 ppm

here lies the debating question. a few papers claim that DO = 0 ppm as anaerobic while a few claim that 2 < DO < 0.05 ppm (which includes zero also) as micro aerophilic 

however, to clearly distinguish the difference between micro aerophilic and anaerobic conditions at such critical situations, go for ORP values.

release of VFA - another sign of anaerobic conditions or decrease in the pH value (only if there's no buffer solution used in the experiment)

Great answers there. Just something additional:

Types of Microbial Metabolism

Aerobic microorganisms: When molecular oxygen is used as terminal electron acceptor in respiratory metabolism it is referred as aerobic respiration. The organisms that exist only when there is molecular oxygen supply are called as obligately aerobic.

Anoxic microorganisms: For some respiratory microorganisms oxidized inorganic compounds such as sulphate, nitrate and nitrite can function as electron acceptors in absence of molecular oxygen; these are called as anoxic microorganisms.

Obligately anaerobic: These are the microorganisms which generate energy by fermentation and can exist in absence of oxygen. They are only active in total absence of oxygen (free oxygen or bound oxygen)

Facultative anaerobes: These microorganisms have ability to grow in absence or presence of oxygen. These can be divided in two types:

(a) True facultative anaerobes: those can shift from fermentative to aerobic respiratory metabolism, depending on oxygen available or not;

(b) Aerotolerant anaerobes: these follow strictly fermentative metabolism and are insensitive if oxygen is present in the system.

Key Reference: NPTEL IIT Kharagpur Web Courses: Wastewater Treatment

If we talk about ecosystems or environments, aerobic is the one where O2 is available, and oxic environments are those where oxygen compounds like NO3, SO4 are available. Thus, anaerobic = lack of O2, and anoxic = lack of other oxidants. Marine sediments under the sulfate zone, where methanogenesis is the only bacterial activity available, is anoxic. Above that zone, where sulfate is present, and upper where NO3 is present are oxic zones. Above these zones are aerobic zone because O2 is available. This is what I have learned.

@Adris Shlimon it is actually the reverse, as explained in the top recommended answer. Oxic environments contain free molecular oxygen (O2). Anoxic environments lack free O2, but may still have bound oxygen as NO3 for example. Anaerobic environments are devoid of all oxygen species, free or bound. In other words, anaerobic conditions are always anoxic, but anoxic conditions are not always anaerobic.

Some of the confusion arises from different usage in different disciplines. Biologists speak of aerobic vs anaerobic respiration to refer to metabolic pathways. Geologists speak of oxic vs anoxic conditions to refer to chemical composition of an environment. Finally, engineers use aerobic, anoxic, and anaerobic to refer to stages of wastewater treatment. My prior post refers to the definitions used in environmental engineering, as I believe it is most likely the context in which the original poster intended the question.