Choosing resistors for an LED lighting panel
... and that they have the same characteristics concerning the forward voltage.

They don't.

Figure 1. Variations in Vf for a typical white LED. Image source: Variations in Vf and binning.

I wonder if the two schematics above are equal.

Nope.

The first one is a classic schedule solution, while the second is an alternative one in order to avoid non-necessary parts.

The LEDs with lower Vf will pass more current and glow more brightly.

I should note that the LEDs will be turned on/off all together, and that they have the same characteristics concerning the forward voltage.

Check the datasheet for the LEDs and look at the tolerances.
My linked article may be of interest.