At will abilities are almost identical to cantrips.
For example I'll cite the Warlock invocations located in the PHB. pg.110.
Numerous invocations have the repeated text:
...at will, without expending a spell slot...
Some have additional requirements, such as Chains of Carceri where the at will ability can not be cast on the same creature without a long rest in between. This does not prevent the caster from casting it on a different creature.
In addition, invocations are separate from spells known. This is important because Warlocks get most of their versatility through invocations due to the limitations on their spell slot usage. Although, they don't have to prepare spells, and have some fairly decent rituals so it's not all bad.
When it comes to Wizard at will spells, the wording is also very specific. I'll use the 18th level Wizard class ability as an example here:
At 18th level, you have achieved such mastery over
certain spells that you can cast them at will. Choose a
1st-level wizard spell and a 2nd-level wizard spell that
are in your spellbook. You can cast those spells at their
lowest level without expending a spell slot when you
have them prepared. If you want to cast either spell at a
higher level, you must expend a spell slot as normal.
By spending 8 hours in study, you can exchange one
or both of the spells you chose for different spells of
the same levels.
This clearly demonstrates that 1) you can cast them without expending spell slots at their lowest level; 2) it specifically states to pick from your spell book, but still requires you to have that spell prepared; and 3) so like Warlock Invocations, these at-will abilities function in the same manner as cantrips (with the caveat that if you want to cast them at higher level, you have to spend the spell slot to empower them.)
If you have any concern with other at-will abilities, please address them in the comments and I will be sure to answer them as soon as capable.