First of all I would like to say I'm unfamiliar with the Mood's test so pardon me if the question is too basic.

I'm trying to compare the difference of median between two groups of data. I did some prelim test first and see that both groups have the same median of 0. These two group have different sample sizes (60k vs 30k observation)

However, my Mood's test in R gives me a p-value of nearly 0 (2.53e-08 to be specific), which I assume mean my two medians are different. So how does this happen when both of my sample's medians are 0 ? 

I have a lot of samples that I want to compare medians together so should I just ignore samples where I found the median to be 0? Thank you.