What explains the differences between doublet verbs that differ by a prefix?

Question

The differences in meanings of doublet verbs such as 3-6 below:

1. Are there any resources that investigate the big picture behind them?
   I abhor to memorise, and prefer to understand, such differences.

2. Are the differences caused only by the prefixes and reflexive pronouns?

3. (s')approcher vs (se) rapprocher : The distinguishing prefix is re-.
   The Spanish translation is not a cognate.

4. (se) paraître vs (s')apparaître : The distinguishing prefix is ad-.
   Similarly, Spanish has two cognates: parecer(se) vs aparecer(se).

5. (se) percevoir vs (s')apercevoir : The distinguishing prefix is À.
   Interestingly, Spanish has only one cognate: « percibir ». English has 'perceive', while apperceive is esoteric compared with the commoner French cognate « apercevoir ».

6. croître vs (s')accroître : The latter's Latin etymon is 'accresco', whose prefix is ad-. Interestingly, Spanish has only one cognate: « crecer ».

Answer 1

These words are called doublets:

In etymology, two or more words in the same language are called doublets or etymological twins (or possibly triplets, etc.) when they have different phonological forms but the same etymological root. — Wikipedia

Yet another, more strict definition, is:

Doublets are cognates within a single language

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The rest of your question is a bit harder.

Bound morphemes, or affixes, indeed, do modify the meaning, but their effect may appear very inconsistent. In other words, a complex word may be not equal to sum of "own" meanings of its morphemes. In languages with more complicated morphology, the own meaning of individual morpheme vanishes even more. Consider Proto-Slavic root *perti (push/carry) in modern Polish:

• przeć (to push) — no prefix
• spór (dispute) — s- usually means "take off from something" or sometimes "join", but here it means generalization of action, and rough etymology appears to be "pressure on each other"
• opór (resistance) — o- means "surround", so the etymology is even less evident: "many people around are pressing".

Unless knowing exact words, it may appear almost impossible to "build" the words from a root and affixes, even if you are familiar with their meanings.

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Summary.
Individual meanings of morphemes may be irregular or vanished in complex words.
The meaning of a resulting word may be too far from sum of meanings of its morphemes.
One can deconstruct an arbitrary word, but it may be hard to construct it from known morphemes.
The only way to know the differences is memorizing.

Answer 2

The prefix often tends to transitivize the verb: while the verb without the prefix can be used intransitively on its own (eg: le renard approche), the prefixed verb cannot by itself

(eg: The following is wrong: ✘ le renard rapproche. ✘).

The prefixed verb needs the reflexive (that absorbs the internal argument and detransitivizes the verb),

This generality is not always true, but is quite general though.