In the first sentence, "white" is used as a modifier (adjective modifier). In the second sentence, it is used as a subject complement.

From the sources/links:

A modifier is a word, phrase, or clause which functions as an adjective or an adverb to describe a word or make its meaning more specific.

A subject complement is the adjective, noun, or pronoun that follows a linking verb. The following verbs are true linking verbs: any form of the verb be [am, is, are, was, were, has been, are being, might have been, etc.], become, and seem. These true linking verbs are always linking verbs.

Shin's answer says it all.

Another reference is here from About Education which says

The adjectives can be written in two ways.

Before a noun
In the end of the sentence using a stative verb

Two examples given there are -

He's an interesting person OR
Jane is very tired.

There is a nice overview of the various ways adjectives and nouns can work together in English here.

As to your specific example, you might find these portions of the cited page especially helpful:

When the information contained in an adjective is not the main focus of a statement, then the adjective is usually placed before the noun in the attributive position.

However, when the main focus of a statement is to give the information contained in an adjective, the adjective is usually placed after the verb in the predicative position, compare:

He handed me a bucket of hot water. (attributive position) I put my hand in the bucket, the water was very hot. (predicative position, emphasising hot.)

and

There are some adjectives which can only be used before a noun, in the attributive position. For instance, we talk about the main problem but cannot say, the problem was main.

Adjectives which occur only in the attributive position are generally those which identify something as being of a particular type. For instance, we can talk about a financial decision where financial distinguishes this from other types of decision, e.g.: medical, political. This group of adjectives are often referred to as classifying adjectives, and rarely occur in the predicative position unless we specifically want to emphasise a contrast, e.g.:

a chemical reaction not, e.g.: a reaction which was/is chemical the phonetic alphabet not, e.g.: the alphabet is phonetic It was an indoor pool. not, e.g.: The pool was indoor

To look at your specific question about the computer:

Your first example, "the white computer," seems to be an instance of a "classifying adjective," as discussed in the second block above: that is, an adjective used to distinguish the white computer from the black one, the gray one, etc. So you would use "white computer" as with "financial decision" in the text above, because you want to specify that you mean the white computer, not the black one or the gray one.

But if you wanted to emphasize the whiteness not just as a classifier but as the most important piece of information, you might say "the computer is white." For example, if someone asked you "Is your computer black?" you would say, "No, it is white."

And if you were using an adjective that provided some additional information about the noun which was not so important either to classify or to emphasize, you might put the adjective before the noun, but probably preceded by "a" or "an" rather than "the," e.g., "I think there is still an old computer in the attic."

Note that there are other special instances to keep in mind, at least some of which are discussed at the linked page.