onnellinen is nominative singular
onnellista is partitive singular
The words that end with -nen drop it and change it into -se- before adding case suffixes.
Here are the cases and numbers we have learnt so far:
Nominative singular: onnellinen koira (happy dog)
Nominative plural: onnelliset koirat (happy dogs)
Partitive singular: onnellista koiraa (happy dog)
Inessive singular: onnellisessa koirassa (in the/a happy dog)
Here are my saved notes from elsewhere on the forums on this very topic:
There isn't a very clear difference between iso and suuri; both mean big or large, but iso is used more with concrete things whereas suuri can be used with both concrete and abstract things.
e.g. Tuo rakennus on iso or Tuo rakennus on suuri (that building is big) are both fine but if you want to say he has a big heart (figuratively) then only suuri sounds correct: Hänellä on suuri sydän.