Now things are getting complicated...
Lesser Celandine (Ranunculus ficaria or Ficaria verna, depending on taxonomic lumping or splitting), in the Buttercup Family (Ranunculaceae), is native to Europe, western Asia, northwestern Africa, and the Canary Islands.
There are also many other yellow buttercups (Ranunculus s.l.).
Greater Celandine (Chelidonium majus), in the Poppy Family (Papaveraceae), is native to much of Eurasia, as well as northwestern Africa.
There are also a number of other, similar, yellow, woodland poppies, such as Chelidonium asiaticum, Coreanomecon, Hylomecon, Stylophorum, etc.
One is a buttercup the other is a poppy. The only similarities between the two Celandines are flower color and general habitat.
As for the question of whether Lesser Celandine is a weed in North America. It is certainly a non-native and could compete with native woodland wildflowers in a natural setting. Still, in a garden setting, it may be an acceptable part of the overall milieu of introduced plants.
However, Ranunculus ficaria is often included on official lists of 'Noxious Weeds'. This is mostly due to the fact that it is toxic and could potentially poison grazing livestock... though so are native buttercups (Ranunculus spp.) and countless other plants native and introduced.