Photosynthesis is a complex process of synthesis of organic food materials. Its is complicated oxidation- reduction process. Here water is oxidised and CO2 is reduced to carbohydrates. It lakes places place in two steps. They are light reaction and dark reaction.

In light reaction ATP and NADPH 2 are produced. In dark reaction CO2 is reduced with the help of ATP and NADPH2, to produce glucose.

In dark reaction, two types of cyclic reaction occur. They are Calvin cycle or C3 cycle and Hatch- Slack cycle or C4 cycle.

Calvin Cycle or C3 Cycle

The Calvin cycle was observed by Melvin Calvin in Chlorella, an unicellular alga. Hence it is called so. In this reaction carbon dioxide is converted into sugars. So it is a process of carbon fixation.
C3 cycle -Calvin Cycle
The first stable compound produced in Calvin cycle is a 3 carbon compound namely 3 phosphoglyceric acid (PGA). Hence Calvin cycle is also called C3 cycle.

Hatch and Slack Cycle
C4 is the alternative pathway of Calvin cycle (C3 cycle) taking place during the dark phase of photosynthesis.
C4 cycle - Hatch Slack cycle
In the C4 cycle the first stable compound is 4 carbon compound, namely oxaloacetic acid. Hence it is called C4 cycle. It is a process of carbon dioxide fixation. This pathway was worked out by Hatch and Slack (1966). Hence the C4 cycle is also called Hatch- Slack cycle.
Calvin Cycle vs Hatch & Slack Cycle 
(C3 cycle vs C4 Cycle)
C3 (Calvin) cycle
1. C3 cycle operates in all plants.

2. The primary CO2 acceptor is Ribulose bi phosphate (RUBP a 5 Carbon compound).

3. The first stable product is a 3-Carbon compound, phosphoglyceric acid (PGA).

4. The carboxylase enzyme is Rubisco.

5. Single CO2 fixation.

6. CO2 fixation is slow and less efficient.

7. Fixation of 1 molecule of CO2 requires 3 ATP and 2 NADH.

8. Only granal type of chloroplasts are involved.

9. Kranz anatomy is absent.

10. Cannot operate under very low CO2 concentration.

11. Oxygen has inhibitory effect of photosynthesis.

12. Sunlight reaches saturation point.

13. Occurs in plants like Mango, apple etc (C3 plants)

C4 (Hatch and Slack) cycle
1. C4 cycle operates only in C4 plants.

2. The primary CO2 acceptor is Phosphoenol pyruvic acid (PEP, a 3 Carbon compound).

3. The first stable product is a 4-Carbon compound, oxalo acetic acid (OAA).

4. The carboxylase enzyme is PEP carboxylase and Rubisco.

5. Two CO2 fixation.

6. CO2 fixation is fast and more efficient.

7. Fixation of 1 molecule of CO2 requires 5 ATP and 3 NADH.

8. Granal and agranal (bundle sheath chloroplast) type of chloroplasts are involved.

9. The leaves have Kranz anatomy.

10. Can operate under very low CO2 concentration.

11. Oxygen has no inhibitory effect of photosynthesis.

12. Sunlight does not become saturates.

13. Occurs in plants like maize, sorghum etc (C4 plants)
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