What are the relationships between those hypotheses in Fine-Grained Complexity Theory?
This is a recent paper introducing Nondeterministic Strong Exponential Time Hypothesis (NSETH), which is an extension of SETH.

NSETH: For every $\epsilon &gt;0$, there is a $k$ such that $k$-DNF-TAUT cannot be solved in nondeterministic time $2^{(1-\epsilon)n}$.

NSETH implies SETH. If NSETH is true, then some problems do not have SETH lower bounds (because they have nondeterministic algorithms faster than deterministic algorithms). 

This paper also introduced Non-uniform Nondeterministic Strong Exponential Time Hypothesis (NUNSETH), a hypothesis stronger than NSETH and SETH.

NUNSETH: For every $\epsilon &gt;0$, there is a $k$ such that $k$-DNF-TAUT cannot be recognized by nondeterministic circuit families of size $2^{(1-\epsilon)n}$.