Let me try to explain the potato thing. Sometimes people with different English accents pronounce words differently, but both are actually correct pronunciations, for the region they're in. For example Americans and British have their own versions of English. (You could argue the British version is more correct if you want, but both are considered to be acceptable English).
For example when Americans say patriotism, they usually pronounce the a as a long a, like in hay, bay, say, and British pronounce it as a short a, as in bat, cat, sat
Potato can be prounced with a long or short a, in a similar fasion, so if someone says potato/potawto tomato/tomawto, they usually mean that they don't see any real significant difference in two different concepts, because they both refer to the same object.
For example, I used to get mad when my mom would call Gulf Coast Toads "frogs", because they were toads, not frogs. She didn't do this, but she could have said "potato/potawto tomato/tomawto" to indicate it didn't matter.