When rolling percentages, do 1d100 and two d10s (percentiles) share the same probabilities?

I know d100s are shunned because they take too much time to roll, and 1d10+1percentile is really fun, but do they share the same probabilities? Is it better to use a (digital) d100?

Also, do d100s have 0? You can’t roll a 0 with percentiles, I think.