Learn English – Can verb ‘grant’ be used with preposition ‘with?’

If you provide for [someone/something in need] without specifying exactly what, it means you make available to them whatever they need - often food (provisions/provender). You can also provide for [some eventuality] without specifying what, meaning you have plans/resources to deal with that eventuality should it come to pass. Both these usages have been around a long time, and always involve for, not to.

To provide [something] to [someone] is a far more recent usage...

Per @JeffSahol's answer, provide X to Y often implies that Y did actually receive X, whereas provide X for Y can be used even if Y doesn't avail himself of the X which is on offer. But often it's an idiomatic choice where people repeat the version they hear most. Other than that, the modern trend towards to clearly disambiguates from the first two usages given above.

Wrap is used as a transitive verb, an intransitive verb and a noun.

As a transitive verb, you wrap something in/by something else or for someone.
For example:

To wrap something IN paper = to use paper to surround something completely (denotes enclosure of one thing by another).
To wrap something BY something = to conduct the wrapping beside something else (denotes a position in space).
To wrap something FOR someone = to conduct the wrapping with a particular intention which relates to another person (denotes an intention).

As an intransitive verb, you wrap up something, meaning to finish or end it.
For example:

We have to wrap up the meeting at 4 o'clock sharp.

The most common uses of 'wrap' + 'with' are where 'wrap' is used as a noun, to denote a rolled-up sandwich, or a shawl, for example.
You'll find plenty of examples here and here.