Twitter API 1.1 and Twitter Search Have Different Results

I worked with Instagram and Facebook APIs and they are doing mostly fine but when it comes to Twitter API, it always becomes headache

Last thing I figured out was that the API 1.1 search has "since" and "until" keywords in the url but they are mostly useless because Twitter Search API looks only for the recent tweets, mostly a couple weeks. After that you can't find your tweet through the API as I experienced in the last 2 months with several testing