Confusion about the Semi-implicit Euler method

On Wikipedia, the page about symplectic integrators talks about how the semi-implicit Euler method is a first-order symplectic integrator.
But when I read the page about the semi-implicit Euler method, they do not show the same algorithm.
https://en.wikipedia.org/wiki/Symplectic_integrator
https://en.wikipedia.org/wiki/Semi-implicit_Euler_method

On the first page, it says

Update the position of the particle by adding to it its velocity multiplied by c1
Update the velocity of the particle by adding to it its acceleration (at the updated position) multiplied by d1
c1 = d1 = 1

Which can be translated to:

$\text{Let g(t, x) = acceleration of the particle at t, x}$ \begin{align} x_{n+1} &= x_n + c_1 * v_n \, \Delta t\\[0.3em] v_{n+1} &= v_n + d_1 * g(t_{n+1}, x_{n+1}) \, \Delta t \end{align}

However, on the second page it is:

\begin{align} v_{n+1} &= v_n + g(t_n, x_n) \, \Delta t\\[0.3em] x_{n+1} &= x_n + f(t_n, v_{n+1}) \, \Delta t \end{align}

Am I failing to see the similarity between the two?

Edit: I've done numerical testing of the two algorithms and they are not equivalent, the first one is not time-reversible. Did I misinterpret something?