Our pipes recently froze and we thawed it out and the water is running but after the water was turned on the toilet started backing up and the tub won't drain. Are these the same problem or are they separate problems? And how can it be fixed? We have already tried plunginh the tub and the toilet.

It maybe that there is still frozen water in a pipe somewhere. You need to remove the water from the tub and use an agitator to try to free the toilet. I think you might have said you did this. You could try using the agitator on the tub too but I'm guessing there is a big slug of ice in some of the pipes and you might need professional help to find it, professionals have devices that can tunnel in the pipes and remove a blockage.

What can happen is there is a buildup of waste, soap or other in a pipe, with a toilet it might be tree roots and it doesn't take much for ice to form and block the pipe. You need to make sure your pipes are regularly cleared

Also drain pipes are larger than the water pipes and will take longer to thaw out.

Definitely look for leaking pipes anytime they freeze after they thaw. Water expands when it freezes frequently but not always cracking pipes.

Are the pipes above ground? If so, then my guess is that the drains froze up. Here, the tub drain has a PTRAP that has standing water in it at all times and I suspect that your toilet may have a slow leaker that allows water to trickle past the flapper at all times and this could lead to a frozen toilet drain pipe (or branch drain).

If this is the case, I would warm water to hot (not boiling) in a tea kettle and then pour that into the tub. Next, I would wait for the water to cool (will cool quickly) and then suck the water out with a wet vacuum. Repeat this procedure multiple times until the water in the trap is thawed and the tub starts to drain. In most of these cases with PVC or ABS plastic drains, the PTRAP will have cracked and will need to be accessed and replaced.

Once you get water flowing in the tub you would run hot water from the tub faucet and see if that thaws the larger toilet drain pipe. If that doesn't work, I would remove the toilet and repeat the hot water/vacuum cycling until the drain pipe is thawed out.

Back to you...

Mark