An operetta is one form of opera, it develops as opéra bouffe or opérette bouffe (for short one act operas) from the opéra comique. The field of operetta is quite wide, and includes stylistic sub genres like the Parisian operetta, the Viennese operetta, the Berlin operetta, stuff like the English Savoy operas, and even a New York operetta. These also differ in time, early Parisian operetta is quite different from late Parisian operetta, Strauß and Lehár are not exactly the same.
So similar to how you have opera singers that specialize in singing Mozart operas, certain styles of baroque operas (one who sings Händel might not sing Monteverdi!), Verdi operas, Wagner operas or whatever you do have opera singers that specialize in singing operetta or more correctly certain styles of operetta. This does not mean that they are not opera singers, and it does not even mean that they will not sing anything outside of their specialization. Per Grundén did sing opera too!
Now about Schlager: One characteristic of operetta is that it tends to be lighter the big operas both in music and plot. This made operetta very popular in the sense of accessible to the people and led to certain numbers becoming hugely popular, similar to a top charts hit nowadays.
So in one direction the operettas were quite close to the popular musical language and in the other direction they did influence it quite a lot (even to the point that quite a few "Jazz classics" actually came from operetta, such as Softly as in a morning sunrise or Anything goes).
But then, early Schlager takes more influences than opera and operetta, you have Varieté music, you have American swing.
Now, Schlager is a fuzzy term, but it usually just means a melody or number that is overwhelmingly popular. With the rise of the Gramophone music became more accessible which fostered the rise of such Schlager melodies, eventually leading to the whole world of commercial Schlager, which is probably what you have in mind. One thing you need to keep in mind about this things is that they are intended for records as main distribution medium, to be played back on Gramophones with very limited dynamic capabilities. So this style is lacking quite a vital part of it’s influences, that is articulation and dynamics.