Reticent means reserved about speaking — holding back what you think or feel. Reluctant means unwilling to do something, anything at all. A reticent witness will not say much; a reluctant witness does not want to be there. Reticent used loosely to mean "reluctant" is common enough to be listed in some dictionaries, but it loses a distinction worth keeping.
The core difference
Both describe unwillingness. Only one is specifically about speech.
- reticent — unwilling to speak or disclose: reticent about her private life.
- reluctant — unwilling to act: reluctant to sign, a reluctant participant.
The drift
"Reticent to invest" and "reticent to commit" appear frequently and are what usage guides object to: the sentence has nothing to do with speech, so reluctant is the word wanted. The looser sense is now recorded in some dictionaries, so it is not exactly an error — but where speech is not involved, reluctant is unambiguous and reticent is not.
The root
Reticent comes from Latin tacere, to be silent — the same root as tacit. The silence is built into the word.