In that picture, the black pipe is 1 1/2 while the beige pipe is 1 1/4. The two sections of pipe were attached by a reducing coupler (behind the leg of the laundry tub). If you compare the size of the black pipe and the beige pipe, you can see that the beige pipe is a little narrower.
All of the beige pipe was 1 1/4, including the section that goes underground.
The previous fittings were labeled 1 1/4 and the new fittings and pipe I bought were all 1 1/4. (that atleast is one thing I can be sure of )
As far as I can tell, the drain is used for the two sinks and is possibly also wet venting a nearby toilet. Probably not good.
As mentioned, I bought the house a couple years ago. I suspect that the drain/vent originally was used just for the laundry tub (and was likely OK for that use), but was tied into for the bathroom which is a more recent addition.