In the US it's not generally about laws unless there has been actionable contact resulting in harm--in practice this is usually about either sexual involvements or financial involvements pre or post termination, with occasional time limits applied.

Short of laws there are state and organizational ethical codes of conduct, some of which are enforced by state boards of practice which can issue sanctions including mandatory surrender of license to practice.

Below these are "recommendations" by professional organizations and state boards: actions that are discouraged, but not generally actionable without proof of harm.

What constitutes "providing therapy services" varies, but many Ts who permit contact that doesn't violate any of the above, put limits on the level and character of their involvement in such contact. So some may refuse to reply, some will reply but not offer advice or comment in a therapeutic way, etc. It really is up to the T to interpret the guidelines.

The greeting issue is usually to protect confidentiality.