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?
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.
Where did the sport of golf come from?
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?
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.