I'm American and had this debate with a Canadian (we're both grammar junkies and were convinced the other was wrong) and we discovered that "til" and "till" are both acceptable abbreviations of "until." (Usually when we disagree on something, it turns out we're both right and it's just local differences!)
When the meaning 'until' is meant for /till/, it is spelled: 'til. "Till" is a verb for treating/opening up the soil in order to plant. I agree, it does not sound natural to use either until or 'til in this context, though. I went with "through." (North American native speaker)
There is a difference. If you tell someone that you are working until Friday. Then you are working on the days before Friday. If you say Monday to Friday or Monday through Friday, then Friday is included. So usually people work on weekdays or work until the weekend. Of course, some people do work on Saturdays.