As far back as the introduction of psionics in Eldritch Wizardry, the psionic saving throw modifiers for the helm of telepathy and the ESP medallion were +4 and -5, respectively. The vast difference in the modifiers brings up a lot of questions, particularly when you consider they are both magic items which essentially do the same thing, though they offer some subtle differences. (BTW, I suggest you read Delta's post "Spells Through The Ages – ESP and Clairvoyance" before continuing.)
In Eldritch Wizardry, the helm of telepathy is afforded the following two advantages (which the ESP medallion is not):
"A helm of telepathy worn by the defender will stun the attacker for three turns if the defender makes his saving throw."
"A helm of telepathy raises psionic strength by 40."
Regarding both the telepathic projection and telempathic projection abilities:
"A helm of telepathy doubles the power and range of the ability and gives the possessor the effect of +4 on his intelligence in addition."
By comparison, the only mention of the ESP medallion in Eldritch Wizardry is the -5 penalty incurred on psionic saving throws.
Now let's take a look at the description of the helm of telepathy from the Monsters & Treasure book:
"Helm of Telepathy: This allows the wearer to read the thoughts of any creature within 9". If his Intelligence rating is greater than that of human or humanoid creatures within the range of the helm the wearer may attempt to control their mind with suggestions implanted telepathically. Such suggestions will have a +2 effect in their likelihood of being carried out (see Vol. Ill for random actions of monsters). For characters in the game roll percentile dice adding 10% to the helm's wearer, and if the character fails to beat this score he will follow the suggestion. (The referee must use judgement here, for a suggestion to kill oneself would not be likely to be carried out in any event.) Treat as non-protective helm if worn into melee."
And now the ESP spell and the medallion of ESP magic item (again, from the Monsters & Treasure book):
"ESP: A spell which allows the user to detect the thoughts (if any) of whatever lurks behind doors or in the darkness. It can penetrate solid rock up to about 2' in thickness, but a thin coating of lead will prevent its penetration. Duration: 12 turns. Range: 6"
"Medallions of ESP: These devices are usable by all classes of characters, even Dwarves, but the device malfunctions on a roll of 6, so whenever in use roll a six-sided die to check it.
Given there is no telepathy spell (a name which is actually much more appropriate than ESP, especially in the context of Delta's comment that ESP as a discipline is a blanket title which includes clairaudience, clairvoyance, and telepathy), the true differences between ESP and telepathy (as abilities) are little to none. The difference lies in the magic items themselves.
A helm of telepathy provides both the ability to read thoughts (an "inbound" ability) and the ability to control creatures (an "outbound" ability). By comparison, an ESP medallion provides only the ability to read thoughts (and, therefore, is an "inbound-only" item).
There's a couple of reasons I really needed to get a handle on the above concepts, rather than simply copying the bonuses and penalties into my system: 1) my system uses a "to hit" model for psionic attacks (which determines initial damage), and 2) this is paired with a saving throw system (used to determine the extent of additional effects).
So what does that mean for these psionic bonuses and penalties? It means that the nature of the helm of telepathy is such that much of what comes in from the outside has a chance of reflecting back upon the attacking creature, but an ESP medallion makes the target more susceptible to the attack in the first place. So here's where I've landed on the copy I'm including at the end of the "Psionic Combat" section of the Basic Psionics Handbook...
MAGIC ITEMS WHICH AFFECT PSIONIC COMBAT
The following magic items provide their users with psionic-like abilities, and each interacts in a specific way with psionic attacks.
Helm of Telepathy: Essentially, this item is “two-way” device (i.e., not only does it receive inbound mental energy, it also sends mental energy out, sometimes enabling the wearer to control the thoughts of a target creature). Therefore, a helm of telepathy gives the wearer a chance to “deflect” an incoming attack and “send it back” at the attacker. In addition to a +4 bonus on all psionic saving throws made while wearing a helm of telepathy, a successful saving throw by a defender wearing a helm of telepathy will create psionic “feedback” which stuns the attacker for 3 turns. Furthermore, any psionicist wearing a helm of telepathy receives a +2 “to hit” bonus on all psionic attacks.
Medallion of ESP: Unlike a helm of telepathy, a medallion of ESP is a “one-way” device (i.e., it only allows inbound mental energy, but provides no recriprocal ability to send mental energy out). This makes the wearer more susceptible to incoming psionic attacks, incurring a -4 penalty to all psionic saving throws while wearing this item.
The +2 "to hit" bonus is my interpretation of the 40 point psionic strength bonus from Eldritch Wizardry. (I don't like the idea that an item provides more mental energy, but do think it offers some kind of psionic potency.) You'll also see I pulled the -5 penalty back a bit to -4.
Considering that the mystic class I've developed has a delicate relationship with magic items (these types of items are rarely allowed, and require the mystic to engage in additional meditation to avoid become attached to them as possessions), and that the monk class I've developed does not possess attack/defense modes (and has a similar relationship with magic items), these may be much rarer occurrences for them they might be in other editions.