The definition of "helminth" (an old term which has no meaning in phylogeny or classification) is "parasitic worm".
The phylum Platyhelminthes includes parasitic and non-parasitic species. "Class Turbellaria" is an obsolete term. The "Turbellaria" is a paraphyletic assemblage, which includes all Platyhelminthes which are not included in the Neodermata.
The Neodermata includes the major groups of parasitic Platyhelminthes (Monogenea, Cestoda and Digenea).
Therefore, to answer the question:
- Turbellarians are not "helminths";
- "Planarians", again a word with imprecise definition, are turbellarians, are not parasitic and thus are not "helminths".
- Parasitic Platyhelminthes (= Neodermata) are all "helminths"
- Parasitic nematodes, acanthocephalans, etc., are also "helminths". But free-living nematodes are not "helminths".
Words associated with "helminths":
Helminthology if the science of parasitic worms - a part of parasitology. Helminthologists study parasitic worms.
Helminthology does not include the study of "turbellarians". Helminthologists do not study "turbellarians".
Exceptions
Note also that a very few species classically included in the "turbellarians" such as dalyelloids or prolecithophorans, are "turbellarians" but are parasitic (Paravortex, Piscinquilinus, Urastoma)... These are exceptions.
Jean-Lou has provided an excellent answer. I will add that while most turbellarians, including triclads such as "planaria", are free living, there are also many species that are parasitic or commensalistic. Most of these live in other invertebrates as hosts, rather than vertebrates. The term, "helminth", typically applies only to worm parasites of vertebrate hosts, including humans and domestic animals. The field of helminthology deals with these.