Pierce invented quite a lot of exotic terminology. “Tychism” (from Greek tyche or chance) is his name for the claim that there is real indetermination in the world. On a philosophical level, Pierce defends the irreducibility of chance. He did some of the early work in probability theory. Moreover, he seems to want to explain cosmological order as an emergent product of evolution from primordial indetermination. He valorizes evolution, and believes in historical Progress.
“Synechism” (Greek “with-having”) seems to be an even more comprehensive scheme, of which Tychism is said to be a part. It asserts not only the irreducible reality but the primacy of continuity over discreteness everywhere. This is related to his relational logic, in which all distinction in what is said is analyzed as part of the verb. Pierce very reasonably understands a grammatical subject as a hypostatization of second-order relations. Synechism draws on the mathematical theory of the continuum and, according to Pierce, on the Aristotelian notion of potentiality.
Synechism was supposed to be the basis of a new Scientific Metaphysics that would be a posteriori rather than a priori. This was apparently a major influence on Whitehead’s process metaphysics, which proposed to replace traditional “Aristotelian substance” with process.
I worry about radical indeterminism, though I don’t think that is what either Pierce or Whitehead intended. I don’t find an emphasis on continuity to be very helpful in matters of historical interpretation, where it is really the differences that matter. Historical Progress sometimes happens locally, but cannot be counted upon.
I like where he is going with the priority of the verb and the deflationary view of nouns, though I would give the place of honor to adverbial expressions. But from what I can tell, Pierce seems to have a pretty linear view of time, including historical time. Pierce and Whitehead both seem to have a rather thin — basically factual — view of actuality. Their evolutionary quasi-teleology is tied up with linear time and a future factual state of affairs.