They are NOT the same equations!!!!!!!!
There is a difference. In the first equation, MATLAB is told that dy is a constant. The NAME of the equation is eq1. This is a quadratic equation with a constant term.
Now, look at the second equation.
You named it dy. dy is NOT seen as a constant here, but a container for the equation itself, much like eq1 was before. Importantly, see there is NO constant term in equation dy.
Note that even though you defined dy as a symbolic variable before, the line:
dy = v0 * t *sin(theta) - 1/2*g*t^2;
overwrites the value of dy. So when you try to "solve" dy, it solves dy by setting it to zero, and solving for t, thus dy==0.
What is the solution there? Clearly, that is either t=0, or t=2*v0*sin(theta)/g.
There is indeed a difference, and it is important to recognize.