Learn Dutch: De twee versies zijn verschillend, niet identiek. - The two versions are different, not identical.

Both translate to "different", but they work slightly differently. You use verschillend when looking at a group of things and saying they have differences among themselves. Anders is typically used when comparing one specific thing to another, often followed by dan (like in anders dan). Here, the two versions are being described together as a group.

Since the lesson covers hetzelfde, could I use niet hetzelfde instead of niet identiek here?

Yes, you can! De twee versies zijn niet hetzelfde is perfectly natural and actually more common in daily speech. Identiek is just a slightly more formal word, exactly like choosing "identical" over "the same" in English.

How would I rephrase this using the een ander(e) ... dan structure from this lesson?

To use that structure, you need to compare one version to the other instead of grouping them as "the two versions". You could say: De ene versie is een andere dan de andere (The one version is a different one than the other), or more simply: De ene versie is anders dan de andere.

I've seen the word verschillende before. Why doesn't verschillend get an -e ending here for the plural versies?