No they aren't but they are similar.
Here are some examples of the two,
As the years pass:
E.g. 'As the year passed, the old couple became more and more dependent on their children.'
E.g. 'As the years pass I feel weaker and weaker (an old person saying this).
The use of 'over the years' is slightly different. It would be used more in general.
E.g. This city has changed a lot 'over the years'.
E.g. 'Over the years' you will learn to appreciate the preciousness of life.
You could also use 'through time' to replace 'over the years'.