The $O()$ notation indicates worst-case running time ("upper bound time complexity").
For example, if we have an unstructured list with $N$ values, then in the worst case it takes $N$ steps to find a specific value in the list and therefore the worst case complexity is $O(N)$ - i.e linear time complexity, for that specific example.
Using simple words - we can be really unlucky such that we will have to go through all the $N$ values of the unstructured list untill we find the desired value.
The $\Omega ()$ notation indicates best-case running time (“lower bound time complexity”).
Looking at the same example of finding a specific value in an unstructured list with $N$ values, the best-case complexity of this operation is $\Omega (1)$ - i.e constant time complexity.
Using simple words - in the best case we can be really lucky and find the unique value we are looking for in 1 try or few tries, doesn't matter how big is $N$. Therefore the best-case complexity is constant for that specific example.
About that question:
(1) Do the O(rdlog2d) and Ω(rd poly logd) have same meaning?
The answer is basically yes, take a look at this explanation for details.