There is no difference between duplicating the effects of a spell and duplicating a spell
This stems from a natural English reading of the words, a spell is its effects. I personally would see no difference between an item that duplicates detect thoughts and an item that duplicates the effects of detect thoughts. If the rules had wanted these to be markedly differently things I feel there would have been some general rule about spells / spell effects being duplicated stating that these are in fact different things. Lacking such a rule, I would conclude that these are identical.
I believe this is further supported by the fact that some, but not all, features that duplicate the effects of something include the line "no concentration required". If this was always the case, then there would be no reason to include such a line. An example of such a phrase is the potion of growth or the potion of speed:
When you drink this potion, you gain the "enlarge" effect of the enlarge/reduce spell for 1d4 hours (no concentration required).
When you drink this potion, you gain the effect of the haste spell for 1 minute (no concentration required).
The fact that these explicitly call out the fact that concentration is not required leads me to assume that without this phrase concentration would be required. Therefore, duplicating an effect of a spell is the same as duplicating a spell, at least when it comes to the concentration requirement.
Another supporting piece of evidence is the Sage Advice Compendium which states:
Q. If a potion doesn’t duplicate a spell, does it require concentration?
A. A potion’s effect requires concentration only if its description says so or if it duplicates a spell that requires concentration.
As far as I can find, every potion that duplicates a spell has the wording of duplicating a spell's effects. Thus, this answer must be about those sorts of potions, otherwise it would be talking about an item that doesn't even exist. From this we can conclude that duplicating a spell is the same as duplicating an effect (or the effects) of a spell, and if the spell requires concentration, so too do the duplicated effects.