How big is the difference in the force between fire hose and tap water water stream? ?

Neither CONTAIN force.  Any force is the result of the interaction of the kinetic energy with an obstacle.  It is possible to burst a pipe with ordinary tap water if the motion can be stopped suddenly.  The force from a water stream is lowered if the outlet size is larger than the tap size so the velocity is reduced. But putting it through a smaller nozzle increases the velocity of the water.  Increasing the pressure on something it hits.  If all other factors were the same ( very rare) the pressure of the water on an obstacle would also be the same so the force would be proportional to the area of the nozzle. If I use a 3mm nozzle and they use a 30 mm nozzle on the same water pressure then the FORCE of theirs would be 100 times greater than the force from my nozzle. Of course if they are using pumps to increase the pressure then the forces would be higher again.

Homes have pressure regulators n their water supplies that protect the plumbing from the high watter pressures from the street. A regulator is usually factory set at 50 PSI. Water flowing from a fire hydrant can be about the same but the volume of water is considerably greater than the 1/2" inch diameter of a water line supplying water to a residential tap. When that larger volume of water is compressed into the diameter of a fire hose the pressure can potentially be increased to between 8 and 20 bar or 116 and 290 psi.

Compare a 5 inch stream of water with a 1/4 inch stream of water.