On the $t$-equivalence of generalized ordered sets

We consider the generalized ordered spaces $X$ and $Y$ such that the tightness $t(X)$ coincides with the tightness $t(Y)$ but $T(X)=\{x\in X : t(x, X)=t(X)\}$ and $T(Y)=\{y\in Y : t(y, Y)=t(Y)\}$ have different cardinalities. Some sufficient conditions are found under which such spaces $X$ and $Y$ are not $t$-equivalent.