G: TL;DR:
Scrambled eggs are emulsified and agitated from the start, while an omelet is set first, then folded. To avoid “chopped-up omelet,” you must prevent the egg from ever forming a cohesive sheet.

Japanese inline (Grade-1 level):
まぜる たまご — mix the eggs
こまかい かたまり — small curds

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The Actual Differences (Direct, No Marshmallow Fluff)

1. Mixing vs. Emulsifying

• Omelet: Light whisk. You just combine yolk + white. You’re not trying to introduce air.
• Scrambled eggs: Vigorously whisk until the mixture is fully homogeneous, slightly foamy, and pale.
  This pre-emulsification prevents sheets from forming later.

2. Pan Temperature

• Omelet: Medium–high. You want the base to set quickly into one large sheet.
• Scrambled eggs: Low to medium-low.
  Low heat = curds, high heat = sheet.
  Any sheet = you’re halfway to an omelet.

3. Butter Timing

• Omelet: Hot pan → butter melts → eggs go in and immediately grab the bottom.
• Scrambled eggs: Butter melts but should not brown. Eggs go in early, before the pan reaches omelet-setting temperature.

4. Agitation

• Omelet: Minimal. You mostly leave it alone until you fold it.
• Scrambled eggs: Constant or near-constant gentle stirring.
  Stirring frequency = curd size.
  • Rapid stirring → tiny creamy curds (French style).
  • Occasional sweeping → tender medium curds (American diner style).

5. Edges

• Omelet: You lift and tilt to let raw egg run under. This builds the sheet.
• Scrambled: You never lift the edges or tilt the pan. That maneuver = omelet logic.

6. When to Stop

• Omelet: Fully set except the top glossiness.
• Scrambled: Stop before fully cooked; residual heat finishes it.
  If you wait until it looks “done,” it’ll be overcooked.

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The Core Principle

Scrambled eggs are defined by continuous disruption of the protein network.
Omelets are defined by allowing the network to form.

Put another way: if you prevent the egg from becoming a sheet for the first 60–90 seconds, you cannot end up with a chopped-up omelet.

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If You Want a Practically Fool-Proof Scramble

1. Whisk hard for 15–20 seconds with a pinch of salt.
   (Salt pre-loosens proteins → creamier curds.)
2. Heat pan on low. Add butter.
3. Pour egg in while the butter is still foamy, not brown.
4. Stir continuously with a silicone spatula, sweeping the bottom.
5. Keep it moving. Break up any sheet the moment it tries to form.
6. Remove from heat when still glossy.

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If you want, I can give you the fastest conversion method: “If you cook like an omelet person, do X/Y/Z differently,” tailored to whatever your omelet habits are.