When there are no identifiable trends in a graph it means there is no relationship between the two variables?

Not necessarily. It could be that the domain and range of the variables is not sufficiently large. For example, if you plotted the ages and heights of boys in a school class you would probably find no identifiable trend. But that is not because there is no relationship between age and height, but simply the fact that the age range is very limited.

With time series data there is also a risk of aliasing. To take rather a contrived example, suppose you have a pendulum with a period of t seconds and you make observations about its location every 3t seconds. You will find that the location remains the same! That does not mean that there is no relationship between time and the position of a pendulum.