What is the difference between "end" and "end)"?

Nothing.

end is still a statement to declare the end of some sort of structure. Like a function, if statement, loop, etc...

The ending parenthesis is simply there to close an argument list.

script.Parent.Touched:Connect(function(p)
    if p.Name == "Dog" then
        print("We touched a dog")
    end -- End to close the if statement
end) -- End and then a closing parenthesis to close the argument list of Connect