2:1 trip rig means that you will get paid the GREATER of the block (flight) time or 1/2 of the duty period. This ensures that if you have a long sit (or several) in the middle of your work day that you don't have a 12 hour duty day with only say 3-4 hours of pay
4:1 trip rig means that you get paid at least 1 hour for each hour away from base (includes off duty rest time on layovers). This means that if you get a 30 hour layover you still get paid.
Trip and duty rigs rarely come into effect. If you have rigs, the company will try to schedule you to avoid activating the rigs...they don't want to pay you to sit on your butt.
But if you DON'T have rigs...stand by for LONG duty days and layovers with no pay. Lack of rigs just encourages the company to schedule crap at their convenience. This is why work rules are vitally important.
Lack of rigs will probably cost you 4 days off each month. You'll be sitting in a holiday inn in the airport industrial zone NOT getting paid... on what should have been a day off.