I am no different ......

"different" is an adjective; "difference" is a noun.

"I am no different in that respect."
在這方面, 我沒有什麼不同。*[不同] is an adjective.

"I have no difference in that respect."
在這方面, 我沒有什麼不同的地方。*[不同的地方} is a noun phrase.

Also, "no different" means "not any different" [沒有什麼不同] , or "not at all different" [沒有任何不同], so it is stronger in meaning than "not different" [沒有不同].

different is an adj. It means the same as somebody; like somebody;eg:-He saw he was no different than anybody else in fighting, in exercising in the gym. Hence "I am no different in that respect."
If difference noun,between A and B is used, then it means the way in which two people are not like each other; the way in which somebody has changed.
Take exercise to translate it to Chinese.