The UK laws elaborate on what is and isn't free speech, while the US law basically just says "there shall be free speech (as far as Congress is concerned. Other parties can do whatever they like to stifle speech)"
UK law is extremely loosely defined. Judges are ultimately responsible for its interpretation, which they do relatively literally - so as long as the police and CPS bring a case there's a good chance you've fallen foul of the law, subjectively - which is how they are written. E.g malicious communications act.
The US constitution is even more loosely defined if you exclude the outcome of hundreds of years of judicial interpretations of it. Hence the endless disagreements over what is or isn’t constitutional.