Why is "has come from" used in this sentence rather than "comes from"?

"Pinewood is wood that has come from a pine tree"

Has come is in the present perfect tense.

If you're unsure what tense you are looking at, you can consult a table of conjugations:

Present perfect conjugation of the verb come from reverso conjugation:

he/she/it has come

What is the significance of the present perfect tense?:

The present perfect is a grammatical combination of the present tense and the perfect aspect that is used to express a past event that has present consequences. - Wikipedia

Relating this back to your example sentence:

"Pinewood is wood that has come from a pine tree"

The meaning here is that the wood has has come from a tree, and this has some consequence now. You might for instance hear someone say this if they were making a case now, for less tree felling, and more preservation of natural resources.

e.g.

"Pinewood has come from a pine tree... Do people not realize this when they go and purchase their trendy new furniture?"

Whereas:

"Pinewood is wood that comes from a pine tree"

Is in the present simple tense, which is:

The tense that is used to refer to events, actions, and conditions that are happening all the time, or exist now. - Cambridge.

You are no longer talking about the past fact that the pinewood was created from a pine tree with present consequences, but simply talking about the fact that pinewood 'comes from' pine trees.

DEFINITION

Your first sentence, "Pinewood is wood that has come from a pine tree" illustrates a formal but idiomatic way of defining something in English.

If I were to ask you the following question,

Where does pinewood come from?

you would likely say,

Pinewood comes from pine trees.

Simple enough, yes? If, however, I were to ask you

What is pinewood?

you would likely say

Pinewood is wood that has come from a pine tree.

What is the difference between the two answers? The second answer, above, is the idiomatic way in English of defining something.

If I were to ask you

What is botulism?

and you wanted to give me a standard dictionary definition, you might say

Botulism is a potentially fatal disease which comes from ingesting food containing botulin, the name for the botulinum bacteria found in imperfectly preserved foods (such as sausage).

If, however, I were to ask you

How does someone get botulism?

you would likely say

You get botulism from eating tainted food.

I guess you could say a dictionary definition is a more pedantic way of answering a question about what something is, whereas a less pedantic and more informal way of answering a question about the same something tends to be more direct and succinct.

One more illustration might be helpful. Question:

What is golf?

Idiomatic answer:

The modern sport of golf is a sport that has come from 15th century Scotland, and it is a club-and-ball sport played outdoors on specially designed terrain.

Question:

Where did the sport of golf come from?

Non-idiomatic answer:

Modern golf came from 15th century Scotland.

STATEMENT OF FACT

Your second sentence,

Much of the opposition to this plan has come from the media

is simply a statement of fact and not a definition. The words has come from express the present perfect tense (or present perfect simple tense). The present perfect tense requires both an auxiliary verb and a main verb.

The auxiliary verb, such as have or has, is expressed in the present tense, whereas the main verb, such as come, is expressed as a past participle. (A participle is a word formed from a verb that can function as an adjective or gerund or can be used to form the continuous tenses and the perfect tenses of verbs. There are two participle forms: the present participle and the past participle.)

Generally speaking, with a statement of fact--which could be, for example, an answer to a question, the questioner is not looking for a definition but for an explanation of what happened or why something happened. Question:

Where does Legionnaire's disease come from?

Answer:

Legionnaire's disease comes from the bacterium Legionella pneumophila and is believed to be spread by inhalation of contaminated water vapor from showers and air-conditioning plants.