In your specific case, "all" is preferable, because it accurately describes the search-pool. "I want to search," the user thinks, "the list of all the clients." I do not think your menu should offer the option to search for "any candidate," since the search should return all the people matching the search criterion, not just some arbitrary one.
More generally, "any," "every," and "all" are sometimes interchangeable, but there are cases where they have different meanings. To illustrate this, they must be translated non-synonymously in some cases symbolic logic, revealing different English meanings. For instance, where “any” and “all” quantify over people:
Same meanings:
- Any people taller than Joe are taller than Mick. (∀x)(Txj ⊃ Txm)
- All people taller than Joe are taller than Mick. (∀x)(Txj ⊃ Txm)
Different meanings:
- If any people are taller than Joe, Paul is. (∃x)Txj ⊃ Tpj
- If all people are taller than Joe, Paul is. (∀x)Txj ⊃ Tpj
Different meanings:
- Joe isn’t taller than all of the people. ∼(∀x)Tjx
- Joe isn’t taller than any of the people. ∼(∃x)Tjx
There is a pattern here. "All" and "any" can be used to express the same quantities when the scope of their quantification is a whole sentence. However, they have different meanings when they quantify over part of a sentence.
The Oxford Dictionary Online defines elucidate as
Make (something) clear; explain:
work such as theirs will help to elucidate this matter
The etymology is reported as
mid 16th century: from late Latin elucidat- 'made clear', from the verb elucidare, from e- (variant of ex-) 'out' + lucidus 'lucid'.
Tracing lucid back, we get
late 16th century (sense 2): from Latin lucidus (perhaps via French lucide or Italian lucido), from lucere 'shine', from lux, luc- 'light'.
Basically, it means shed light on.
ODO defines explicate as
Analyze and develop (an idea or principle) in detail:
attempting to explicate the relationship between crime and economic forces
The origin is reported to be
mid 16th century: from Latin explicat- 'unfolded', from the verb explicare, from ex- 'out' + plicare 'to fold'.
The sense it to unpack or unfold a complex concept or relationship.
While there is a great deal of overlap, and either might fit many circumstances, there are subtle connotatve differences. Elucidate might be a better choice when some information, perhaps only a single fact, reveals the nature of the situation. Explicate would seem better suited when a process of unraveling a complex situation is necessary to get to the truth or to understanding.
Were I to tell someone I hate my brother, I could elucidate by saying He beat me up every day when I was a boy.
Or I could explicate by tracing the 70 year history of complex business transactions, contested inheritances, joint ventures, competitive projects, political campaigns and the battle over a betrothed that slowly turned sibling camaraderie to contempt.
Best Answer
According to Washington State University Emeritus Professor of English Paul Brians' book Common Errors in English Usage, select is to convey high quality and selected is to convey a specific subset.