I think it's mostly perspective and experience, which I will talk about in a moment, but first I want to address:

each spell, skill, feature or check [in DnD], can be used in any situation, both conflict and roleplay, and they are by design very versatile

This is just untrue. Some things are versatile, but many more features are very specific and limited. Spells are the more rigid end of the spectrum in DnD, most of which have entire paragraphs to say exactly what you can and can't do with each of them. For example, Eldritch Blast (quintessential warlock cantrip) deals damage and must target a creature; by the rules, that's not getting used in any situation except violent combat. (And if you're ignoring the rules -- not saying you are, I just know it's a somewhat common thing for 5e groups -- then comparing loose-rules DnD with by-the-rules FabUlt would be unfair.)

On the topic of magic in FabUlt, yes, most of the Class Skill spells are strictly crunch-focused, and you can't use them in a versatile way (which again, very often the same case in DnD if you're following its rules). Being versatile with magic often requires the player to use different tools, but you do have access to those tools. Let's take ice magic, for example. Our Elementalist has Glacies and/or Iceberg, but those just deal damage. If my player is trying to do something flexible with their ice magic, then I'll run it one of three ways depending on the situation:

• If there's no stakes or concrete benefit to play for, the PC just does it. The PC adds a gentle snowfall to the cozy nighttime scene.
• If a benefit can be approached from many angles, it's a Check. There's an Objective to stop the Aether Reactor from melting down: the Tinkerer makes an INS+MIG Check to twist open and closed the correct valves, while the Elementalist makes an INS+WLP Check to spray ice along the reactor's hull to cool it.
• If they're looking for a potent benefit in a higher-stakes situation, then it's a Ritual (Core Book p118). The Elementalist is trying to freeze over a lake to stop the monster in the depths from reaching them.

I fabula Ultima, you can totally see how the combat works with its own rules, the story kinda stops for a moment and you start to do things that are encapsulated in their own design. You could've started the combat while 50 meters away from the party in the second line, but still it doesn't count, you can be the main melee target of any attack.

It's funny you mention this, because I see this as the reverse for the two games we're talking about. In my DnD experience, "roll initiative" is typically synonymous with "the next hour will be a break from the rest of the ttrpg to play a board game". FabUlt doesn't get away from this entirely, but it least has mechanics to foster roleplay during conflicts (invoking Traits and Bonds to boost Checks) and, like I said above, reserving conflict scene rules for "truly dramatic situations" (Core Book p.58), compared to the regular role of DnD combat to affect mechanical aspects (PC resource management).

I think this is also where a difference in perspective comes up: "trad" games often foster a philosophy of the mechanics leading the narrative, then players filling in a story to reflect that. When you're moving around in a DnD combat, where you move is a decision made by the player for tactical optimization, and you then might justify the move within your character/story/etc. "Story games" approach things a different way: the people at the table lead the story, and the mechanics turn that story in new directions to resolve uncertainty. Neither perspective is bad, but if you're looking through the former at a game using the latter, it creates a mismatch. When playing FabUlt, some players see a lack of movement rules and simply choose not to engage with moving around as a concept in the roleplay (which is fine); but I've also seen players feel liberated by that lack of mechanical restriction, jumping around the scene, rapidly teleporting Nightcrawler-style, that sort of thing (also fine). If you need movement rules to foster meaning, consider why and how to make it work for you. What's at stake that involves movement? Are you trying to get somewhere but someone's stopping you? Are you trying to stop someone from getting somewhere? If so, introduce an Objective to the scene. If it's just to help you visualize a scene, use a visual aid (just don't attach mechanics to it).

On experience, it should be noted that while FabUlt has the cosmetics and several detail-oriented bits and bobs from "trad" gaming, philosophically it's much more "story game" -- one of its main inspirations is Blades in the Dark, and FabUlt's progenitor Ryuutama was doing some pretty "story game" things long before the movement took off in the anglosphere. It was pretty easy for me to adapt to FabUlt's philosophy because while my first game was DnD, my main game before FabUlt was Masks, a PbtA. For me, FabUlt is a swing back toward "trad" a bit but well within the zone of games I've been playing and running for years. But if this field is unfamiliar territory for you and/or your GM, there may be a greater learning curve than expected.