That’s a very broad topic… I’ll try to answer your question in a few lines:
Aluminum salts such as alum and poly-aluminum chloride (widely available under different trade names) are coagulants not flocculants.Other types of coagulants are iron-based: ferric chloride, ferric sulfate, ferrous sulfate, etc. Both destabilize suspended colloidal particles in order to allow for aggregation. The choice of coagulant depends on the water to be treated (TOC, hardness, turbidity, and pH as well as iron, aluminum, manganese, calcium and chloride content), the temperature of the water (summer or winter), its calco-carbonic equilibrium, and last but not least the treatment results you want to obtain (removal of turbidity and/or NOM, iron, arsenic, etc.). So jar testing has to be performed in order to find the right coagulant for the water.
A flocculant can be an anionic, cationic or nonionic organic polymer (again available from different suppliers). Increasingly, green or natural polymers such as starch or alginate are being used. They allow for larger and heavier floc. You will also have to jar test to choose the right flocculant. The choice of sludge treatment (dirty water from filter cleaning and decanter purging) can also affect the choice of the coagulant. All kinds of solutions have been tested and implemented over the years, so it’s impossible to summarize them all for the purposes of this forum. Some plants use aluminum sulfate; others rely on PAC or ferric chloride. Some combine the two depending on the type of water and the season.