I thought that site explained it pretty well, but I'll rephrase it just in case:..
We use prefer to say we like one thing or activity more than another. We can use a prepositional phrase with to when we compare two things or actions:
I prefer tea to coffee.
We prefer going by ferry to flying.
We use would prefer or ’d prefer, followed by a to-infinitive or a noun, to talk about present and future preferences:
I’d prefer to go by myself.
Would you prefer a quieter restaurant?
She’d prefer not to drive at night.
So, 'I prefer' means 'I like x more than y.' The comparison can be implied to include all possible options in that category by omitting 'more than y,' as in your example:
She prefers to drink tea.
This means that, as a general guideline, she would rather drink tea than any other beverage. Context can also imply a more specific comparison:
Jim: Have you been to Coffee Unlimited? They have really great coffee.
Sue: No, I prefer tea.
Given the context of coffee, this means that she, as a general guideline, prefers tea over coffee.
We use 'would prefer' to specify a specific occasion:
She would prefer to drink tea.
This means that, in this particular instance, she would rather drink tea than a different beverage. This does not imply that she always prefers tea, just that she would prefer tea in this particular instance.
Here's an example conversation:
Tom: Let's go out to Paddy's Pub tomorrow.
Andrew: We should invite Beatrice too.
Simon: Doesn't she prefer wine? Paddy's wine selection is very overpriced.
Andrew: Yeah, but she likes chocolate stouts almost as much. She would probably prefer to get chocolate stout rather than overpay for bad wine.
As stated, Beatrice in general prefers wine, but specific to this scenario she would rather have an chocolate stout.