Why does aluminium chloride react with water in 2 different ways?
Yes, adding a small amount of water to anhydrous AlCl3 is different from an aqueous reaction. Here is an excellent educational institution's answer in the first case, depicting the action of water on anhydrous aluminium chloride, to quote:

If a small amount of water - a few drops - is added to anhydrous aluminium chloride there is a hissing sound and hydrogen chloride gas is given off as steamy acidic fumes. The reaction that occurs will depend on the amount of water added, but is probably
$\ce{AlCl3(s) + H2O(l) → AlCl2OH(s) + HCl(g)}$

In the second case, aluminium chloride in aqueous solution appears to undergo a two-stage reaction, starting with the formation of the hexaaquaaluminium ions, to quote again:

If aluminium chloride is dissolved in a large amount of water the solution is acidic, but this has nothing to do with formation of hydrochloric acid. The solution contains hydrated aluminium ions and chloride ions:
$\ce{AlCl3(s) + aq → [Al(H2O)6]^{3+}(aq) + 3 Cl -(aq) }$

This is followed by an acidic hydrolysis paralleling transition metals:

The hexaqua complex ion behaves exactly like ions of similar type formed from transition metals; the small, highly charged metal ion polarises (withdraws electron density from) the water molecules that are attached to the aluminium ion through dative covalent bonds. This makes the hydrogen atoms d+ and susceptible to attack from solvent water, which is acting as a base. The complex ion is deprotonated, causing the solution to be acidic from the formation of hydroxonium ions H3O+:
$\ce{[Al(H2O)6]^{3+}(aq)  + H2O(l) →  [Al(H2O)5OH]^{2+}(aq) + H3O+(aq)}$