Jordan form and determinant divisor or elementary divisor

Question

Say let there be three matrices $X_1,\,X_2,\,X_3$ whose Jordan form are \begin{equation} P_1^{-1}X_1P_1= \begin{pmatrix} \lambda & 0 & 0 \\ 0 & \lambda & 0 \\ 0 & 0 & \lambda \end{pmatrix} ,\quad P_2^{-1}X_2P_2= \begin{pmatrix} \lambda &1 & 0 \\ 0 & \lambda & 1 \\ 0 & 0 & \lambda \end{pmatrix} ,\quad P_3^{-1}X_3P_3= \begin{pmatrix} \lambda &1 & 0 \\ 0 & \lambda & 0 \\ 0 & 0 & \lambda \end{pmatrix} . \end{equation} I understand that for each matrix there are 3,1,2 linearly independent eigenvectors.
Is there any difference between these in terms of determinant divisors or elementary divisor?
I ask this question from curiosity.
Thanks.