The word "hätte" is conditional, which means something would have happened in a certain/different scenario. The word hatte represents a truth that really happened.
Here's an example:
Hätte ich einen Feuerlöscher gehabt, wäre das Haus nicht
niedergebrannt. If I had had a fire extinguisher, the house wouldn't
have burned down to the ground.
Ich hatte einen Feuerloescher, weswegen das Haus nicht niedergebrannt
ist. I had a fire extinguisher, so the house didn't burn down.
Also the word hätte is the conditional tense of the word haben, which means it can be used in any time period. The word hatte can only be used if something has already happened.
Hätte ich mehr Geld, würde ich ein Auto kaufen. If I had more money,
I would buy a car.
(Notice this conditional sentence is set in the presence)
The difference between wurde and würde is easiest to explain by translating them. I guess the other answer stated that it is difficult because the words look so similar that you could assume that they are alternations of the same word like "hatte" and "hätte". BUT THEY ARE NOT.
Würde means would (NOT should!!!) and wurde means became or in some case was. Nothing else.