First, as the nouns in your example sentences are countable you need to use 'many' and not 'much'.
Then the difference in meaning between the sentences using 'as many as' and those not using it can be understood as follows
- Police fired a total of 20 shots at the car. Exactly 20 shots were fired.
- Police fired as many as 20 shots at the car. The number of shots fired is uncertain but not more than 20.
There is a similar difference between the sentences in your second example.