Desmos is plotting (sinx(1+x)-sin(x)) as a step function(discontinuous function) when zoomed to precision of 10^(-16)
But (sin(1+x) - sin(1)) is continuous function over entire real line.
And here is screenshot of plot :-
Your browser uses a number type that can only take on a finite number of values. This means that zooming in enough reveals jumps between discrete values. What you’re seeing are the most precise values that exist in the calculator (there are no numbers between those numbers!) Here’s another example.