Let's start with the end of this sentence—the list of heresies. These can actually be classified under one or another of the descriptions you've highlighted.
A greater or a less
Arianism used the text of John 14:28, "The Father is greater than I", to argue that the Son of God was not truly God, but a lesser being who was begotten after God the Father. His belief was pronounced heretical by the First Council of Constantinople in 381.
Something corporeal or corporeally conceived
In this area go the Anthropomorphites, who appear to have believed based on Genesis 1:27 that God had a literal human form, a physical body. In addition, this group includes some of the Monarchians. Monarchianism generally is the belief that God is one ruler, not three; it is opposed to Trinitarianism. Some Monarchians apparently believed in a variant of Adoptionism, stating that Jesus was born a human being, but was granted divinity later in his life.
Note: "Patripassian" appears to have been a name given to certain Monarchians in virtue of their belief that God is one and not three. Trinitarians argued that by this line of reasoning it was the Father (Latin pater) and not the Son who had suffered (Latin passus) on the cross.
Something different with respect to character or will
One could put Arianism here, believing that the Son was "something different" from the father. In addition, under this head go the followers of Aëtius of Antioch, who believed that the Son is "of similar substance", but not "of the same substance" (in Greek, homoiousios but not homoousios) as the Father. Finally, the followers of Macedonius I of Constantinople appear to have believed that the Holy Spirit was a servant of the Father, created by the Son, but not divine himself.
Something mixed or solitary
The Arians, Macedonians, and Aetians could all be considered as believing that God was "mixed or solitary"—in their case "mixed", in the sense that they all believed that the Son or the Holy Spirit was not "one with", that is "of the same substance as", the Father.
The Monarchians (among whom are included Paul of Samosata, Praxeas and Sabellius), on the other hand, believed that God was "solitary"; that is, that God was One but not Three.
The only ones left are the Novatians. I took a look on Wikipedia, because I hadn't heard of them before. Apparently their primary heretical belief was that Christians who, for fear of persecution by the Romans, had renounced their belief or sacrificed to pagan gods, should not be accepted back into Christianity. I don't see that belief fitting into any of these categories; I'm not certain why they are included in this list.
Chapter III of the Second Helvetic Confession is intended to declare a belief in God as Unity in Trinity:
the same immense, one and indivisible God is ... distinguished as Father, Son and Holy Spirit so, as the Father has begotten the Son from eternity, the Son is begotten by an ineffable generation, and the holy Spirit truly proceeds from them both, and the same from eternity and is to be worshipped with both. ... there are not three gods, but three persons, cosubstantial [sic], coeternal, and coequal; distinct with respect to hypostases, and with respect to order, the one preceding the other yet without any inequality.
This list of heresies names people and groups who (generally in the second to fourth century, as the Church was refining its teachings on who and what God was) had other ideas later declared heretical; and the list of characteristics you've pointed out simply describes more or less what those ideas were.