The description of Ioun Stones reports:
Thereafter, another creature must use an action to grasp or net the stone to separate it from you, either by making a successful attack roll against AC 24 or a successful DC 24 Dexterity (Acrobatics) check.
Is the "successful attack roll against AC 24" specific to using a net to take it, or can you take it with a successful attack roll of any sort?
Net as a verb in this context means:
to succeed in getting something of value, esp. as the result of a plan of action
The context is a specific action, and that you either grasp or net makes this explicit:
must use an action to grasp or net the stone to separate it
and you can achieve this:
either by making a successful attack roll against AC 24 or a successful DC 24 Dexterity (Acrobatics) check.
hence you do not need to make an attack roll with a net, but an Attack Roll:
When you make an attack, your attack roll determines whether the attack hits or misses. To make an attack roll, roll a d20 and add the appropriate modifiers. If the total of the roll plus modifiers equals or exceeds the target's Armor Class (AC), the attack hits.
The AC that you need to equal or exceed with your Attack Roll is 24. Or you alternative make a regular DC 24 Dexterity Acrobatics check.
Thereafter, another creature must use an action to grasp or net the stone to separate it from you, either by making a successful attack roll against AC 24 or a successful DC 24 Dexterity (Acrobatics) check.
The only way to separate the stone from its owner (without destroying it) is to "grasp or net" it. While "net" has multiple meanings as a verb, by far the most common and most relevant in this context is the obvious: to catch something in a net.1 So, hitting the stone with any attack capable of grasping or netting it will do so. Hitting with any other attack will have that attack's normal effects (typically dealing damage to the stone).
So, what kinds of attacks fulfill this requirement? Certainly an attack with a net qualifies. You could make an argument that an unarmed strike with a free hand could grasp the stone, but I think the more reasonable ruling in that case is for the DM to treat it as a Dexterity (Acrobatics) check rather than an attack roll.
Arguably, any attack that can target objects and that inflicts the grappled or restrained conditions on a hit should also be eligible to grasp or net the stone. Although conditions, including grappled and restrained, are only meaningful for creatures, the fact that an attack inflicts one of these conditions indicates that it is an attack capable of grabbing or grasping. (Note that an attack with a net also fulfills this criterion.) For example, a giant crab's claw attack is made against "one target", so it could grasp the stone by attacking it, though with only a +3 modifier, it will need a natural 20 to succeed (and it will deal damage for a critical hit in addition to grabbing the stone). However, a constrictor snake's constrict attack targets "one creature", and hence cannot grasp the stone.
Conversely, attacks capable of causing forced movement should probably not be able to separate the stone from its wielder, since pushing or pulling is not the same as grasping or netting. Also, effects that involve a saving throw or ability check instead of an attack roll cannot affect the stone, with the sole exception of a Dexterity (Acrobatics) check.
Ultimately, it's up to the DM to decide which attacks are capable of grasping or netting the stone. A net attack and a sword attack are easy cases to decide, but a pincer claw, a bite attack, a tentacle grab, a roper tendril, etc. are more ambiguous cases not clearly spelled out in the rules, which means we fall back on the 5e principle of empowering the DM to fill in the gaps.
1The more general, figurative use of "net" as a synonym for "acquire" is almost exclusively reserved for financial and figurative contexts and is typically used with a different syntax, e.g. "selling my Ioun stone netted me 5000 pp". This definition is almost never used in reference to physical objects, and is almost certainly not the intended interpretation in the context of taking physical possession of an object.
The description of the Ioun Stones specifies how a creature can safely remove the orbiting stone around the head of another creature: by capturing it, using their hand(s) or using something to catch it (such a net, or even a simple bag, for example). This approach requires an action which involves an attack roll or a DEX check.
In the description one can find this further sentence (emphasis mine):
A stone has AC 24, 10 hit points, and resistance to all damage. It is considered to be an object that is being worn while it orbits your head.
Note that the AC is 24: the very same value reported in the previous lines and equal to the DC of the DEX check. Since it is possible to attack worn/carried objects (considering the explictly stated exceptions, e.g. targetting with Light cantrip), the Ioun stone can be attacked via classical attack rolls, since its AC is clearly stated. This is confirmed by the fact that the Ioun stones' description does not explicitly prevent to attack the orbiting stones.
The main difference is that the description lists the way in which a creature can safely remove the orbiting stones from the opponent's head without damaging it, while a classical attack may completely destroy the stone. Indeed, one may find the following paragraph entitled Magic Item Resilience in the DMG (pag 141, emphasis mine) :
Most magic items are objects of extraordinary artisanship. Thanks to a combination of careful crafting and magical reinforcement, a magic item is at least as durable as a nonmagical item of its kind. Most magic items, other than potions and scrolls, have resistance to all damage. Artifacts are practically indestructible, requiring extraordinary measures to destroy.
which supports the above ruling: indeed, the emphasised part implies that a magical item can be damaged, unless stated otherwise.
In this particular situation, a DM may adapt the rules for Knocking a Creature Out for giving to players the chance to not destroy the Stone:
Sometimes an attacker wants to incapacitate a foe, rather than deal a killing blow. When an attacker reduces a creature to 0 hit points with a melee attack, the attacker can knock the creature out. The attacker can make this choice the instant the damage is dealt. The creature falls unconscious and is stable.
When the blow that would destroy the stone is struck, the character may decide to hit the stone aiming to throw it away from the enemy's head, without destroying it, for example hitting it with the flat part of a greatsword.
