Is the telepathy rule in the Monster Manual only applicable to monster telepathy abilities?

Question

In the introduction to the Monster Manual (p. 9), the description of telepathy states:

Telepathy is a magical ability that allows a monster to communicate mentally with another creature within a specified range. The contacted creature doesn't need to share a language with the monster to communicate in this way with it, but it must be able to understand at least one language. A creature without telepathy can receive and respond to telepathic messages but can't initiate or terminate a telepathic conversation.

A telepathic monster doesn't need to see a contacted creature and can end the telepathic contact at any time. The contact is broken as soon as the two creatures are no longer within range of each other or if the telepathic monster contacts a different creature within range. A telepathic monster can initiate or terminate a telepathic conversation without using an action, but while the monster is incapacitated, it can't initiate telepathic contact, and any current contact is terminated.

Are these rules intended only to apply to monsters' telepathic abilities?

Specifically, when it says:

A creature without telepathy can receive and respond to telepathic messages but can't initiate or terminate a telepathic conversation.

Does that mean that characters can respond to "a monster's telepathic messages", or "telepathic messages from any source"?

Several Jeremy Crawford rulings seem to imply that the intent is for this to apply only to monster telepathy (see two March 2017 tweets here and here, for example). However, I've seen this cited in arguments that have nothing to do with monster telepathy as well (see this answer to "Is the Warlock's Awakened Mind telepathy two-way, or only one-way?"). So I just want a clear answer as to what case this section of the rules applies to.

Answer 1

Monsters only

You are quoting a passage from the Monster Manual that specifically talks about Monsters within it. There is no reason to apply those telepathic abilities to a PC without an equivalent from the DMG or PHB or another character based reference.

In addition, the Sage Advice clarification on Awakened Mind states:

In contrast, the telepathy ability that some monsters have (MM, 9) does make two-way communication possible.

This clearly differentiates the Monster telepathic ability from others.

Responding to Monster telepathy

Yes, a PC can respond to a Monster using telepathy as stated in the quote provided in the question (MM, 9)

A creature without telepathy can receive and respond to telepathic messages but can't initiate or terminate a telepathic conversation.

Answer 2

It applies only to monsters.

People sometimes mistakenly assume that unrelated abilities that share similar names must follow similar rules, which is not the case at all. In actuality, the wording applies in the situations it says it applies. If another feature is intended to work the same as an existing feature, it will call it out.

The only time a player ability would work the same as monster telepathy is if it contained wording such as "telepathy (as the monster ability)" or something along those lines. Otherwise, the rules for telepathy given in the Monster Manual only apply to a monster's (or NPC's) telepathy.