What are the different types of structural connection bolts that are commonly used in the steel construction?

Ordinary Bolts (Carbon Steel Bolts):

Grades4.6 ,4.8 ,5.6 ,5.8 ,6.8 

High Strength Bolts (Heat Treated - Carbon Steel Bolts): 

Grade8.8

High Strength Bolts (Alloy Steel Bolts): 

Grade10.9

***** In my opinion Grade8.8 is the optimum because of : 

               1- Carbon steel

               2- Plastic Range=160 Mpa or High Elongation Percent Relative to Strength

               3- Carrying Static Loads and dynamic loads

Commonly Used Bolts are Grade8.8 and if high strength Bolts are required in any particular area/project Grade10.9 can also be used.

Bolts differ in grade for example Grade4.8 or Grade8.8

They also depend on size eg M10 ,M12 etc

What type to use really depends on the type of connection , force to be restrained number of bolts that have to resist stresses and bolt configuration or layout.