The short answer
Brut is the drier category, Extra Dry the sweeter one. The English word is misleading: it sounds especially dry but actually means the opposite.

From bone-dry to sweet: the order
For sparkling wine, Brut Nature and Extra Brut sit at the driest end. Next come Brut, Extra Dry, Sec, Demi-sec, and Doux. The dosage largely determines the perceived sweetness. But how balanced a bottle ultimately feels also depends on the wine itself.
The order seems counterintuitive. "Dry" means dry in English, and "extra" sounds like an intensifier. That's exactly where the buying mistake happens: Extra Dry sits one step sweeter than Brut, not one step drier. So memorize the whole sequence as a fixed order. Focus on its position within the sequence rather than the individual word. Here's a simple trick: say the whole sequence out loud once, from dry to sweet. Extra Dry then audibly falls right after Brut.
Dosage is the sugar addition that helps shape a bottle's style. It doesn't explain everything, though. A wine with high acidity will feel tauter and leaner at the same dosage level. A softer wine with the same dosage will feel rounder and fuller. That's why a Brut from one house can taste mild to you, while a Brut from another comes across as distinctly austere.
What this means for your shopping
If an Extra Dry bottle was too sweet for you, Brut is the next direction to compare. If a Brut struck you as too harsh, you don't have to train yourself into liking the supposedly more sophisticated taste. Find a variant you actually prefer. There's exactly one step between the two, so the jump is small.
Don't thoughtlessly apply these terms to still wine. There, the terms follow a different classification. For a fair comparison, note down the exact label statement and your impression in the glass. That way you'll know later whether you're really buying the same style again.
The statement rarely appears prominently on the front label. Usually you'll find it in small print beneath the name or on the back label, sometimes at the edge of the foil capsule. Brand names and range names say nothing about the sweetness. If you're unsure in the shop, look specifically for one of the words in the sequence. Everything else on the label can wait.

Brut or Extra Dry: which label helps you?
From this overview, take away a single word to look for on the shelf. It doesn't spare you the tasting. But it does narrow the choice considerably. That one word gets you closer to your taste than any flavor description on the back label.
| Your preference | What to look for |
|---|---|
| The drier of the two categories | Choose Brut |
| A touch more sweetness possible | Compare Extra Dry with Brut |
| A specific flavor expectation | Also taste for acidity and overall style; the category alone doesn't describe everything |
Why "Extra Dry" is sweeter than "Brut"
Drier doesn't mean better. The steps on the scale describe a style, not a quality level. A bottle with noticeable sweetness can be carefully made. A very dry one can bore you. Anyone who forces themselves toward the more austere taste because they consider it more sophisticated usually ends up enjoying it less in the long run.
The second misconception concerns what you expect from a single word. "Brut" describes a range, not an exact point. Two bottles with the same label statement can differ noticeably in the glass, because acidity and aging shape the impression too. So the statement narrows down where you'll land. It doesn't fix it precisely.
How to find your range
Buy two bottles from neighboring steps and open them the same evening. Same temperature, same glasses, small pours. Have someone pour them for you blind, so the label doesn't influence your taste. Try both twice: once right after each other and once after a pause.
Afterward, write down more than just "better" or "worse." Note what struck you: does one seem too austere on the finish, the other too broad? This short note, together with the exact label statement, is worth more at your next purchase than any general recommendation. It maps out your own personal taste.