The 1871 Census for Watt(which appears on two separate pages) shows an Elizabeth age 8 and an Anne age 3. The 1881 Census lists them as Elizabeth age 17 and Eliza Anne age 12 so yes, they are two different people. I have found nothing to say that Elizabeth's middle name was Marie or Maria or even Nancy - still looking for that data. The family bible that is transcribed on this thread lists Elizabeth as only two years older than Eliza and is the only place I have seen the middle name of Maria used - but it is a typed transcript so I really don't know that it is accurate.
Hope this helps!