In theory, if you look up the official dictionary for Spanish, they are equivalent. If you look up "repartir", they define it with "distribuir". Having said that, at least in Latin America, there are subtle differences in my opinion.
In my experience, "distribuir" is used way more often in a business sense, having to do with logistics and supply chains.
"Hay que distribuir el producto en todo el país." = We have to distribute these products all over the country. ( In this case, you can also use "deliver" in English )
On the other hand, "repartir" is used, at least as I feel it, more in the sense of giving in equal parts, almost "sharing", e.g.
"Reparte los dulces entre todos los niños." = "Share ( or divide ) the candies among the kids. "
You wouldn't really use "repartir" to talk about delivering merchandise, although the idea would be understood.
Other uses of "distribuir" in Spanish are similar to English:
"Hay que distribuir bien el peso para no perder balance." = We have to distribute the weight carefully to avoid loss of balance.
"Hay que distribuir las ganancias entre los accionistas." = We have to distribute profits among the shareholders.
I have to say, though, that in these two last examples, you could use "repartir" and it would be understood.