You're not likely to mix up the meaning of wurden with würden (or konnten with könnten) when reading or having a conversation in German, as the context makes it pretty obvious what is meant. But I've noticed occasionally when writing in German that it's important to have a clear sense of the difference between the two.
The words wurden and konnten are the Präteritum / Indikativ (preterite / realis) moods of the verbs werden and können, respectively. The words würden and könnten are the Präteritum / Konjunktiv II (preterite / subjunctive) moods of the verbs werden and können, respectively.
But all grammatical complications aside, an easy way to remember the difference is that these verb forms do not use the umlaut letter when talking about the actual past, and both words do use the umlaut letter when talking about the conditional present or future.
Sie flohen aus dem Königreich und wurden nie wieder gesehen.
They fled from the kingdom and were never seen again.
Caption 85, Märchen - Sagenhaft - Das tapfere Schneiderlein
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Wir würden gerne auf 'ne kleine Clubtour geh'n.
We would like to go on a small clubs tour.
Caption 17, Deutsche Bands - Die „No Angels“
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Die hungrigen Kinder konnten es kaum erwarten, davon zu essen.
The hungry children could barely wait to eat from it.
Caption 61, Märchen - Sagenhaft - Hänsel und Gretel
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„Wir könnten unendlich so weiterlaufen“, antwortete Frederick.
"We could continue walking endlessly like this," answered Frederick.
Caption 10, Piggeldy und Frederick - Unendlichkeit
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Got it? An easy way to remember with wurden/würden and konnten/könnten is: if an umlaut letter is present, you are talking about the possible present or future!
Further Learning
Visit Yabla German and watch the two Yabla videos conjugating the verbs werden and können and practice writing some of your own sentences using the different tenses of the verbs.