There is only one official definition of unemployment—people who are jobless, actively seeking work, and available to take a job (from BLS)
Why would someone on welfare and seeking a job not be considered unemployed ?

That may be the official definition but let's get practical here for a minute. If you are on the dole and putting in job applications at McDonalds, how can the government track this? I have not GOOGLED this, but it seems to me that the easiest way for the government to determine whether or not you are unemployed is by checking its records to see if you are collecting an unemployment check. Collecting a welfare check is not the same thing.