I think because both can be translated as How in English. So if it's related with Verb It will be 어떻게. Because usually people consider or ask 어떻게 하니 'How to do it' If it's engaged in other Adjective, it will be 얼마나 such as 얼마나 기니 How tall, 얼마나 많이 How many. Ex) 학교에 어떻게 가니? How to I get to the school? 학교가 얼마나 머니? How long does it take from here to school?

I find it hard to see the similarities other than that they are translated to "how". Their functions are entirely different.