Is the aircraft now IFR?
The only way ATC can initiate an IFR clearance is by saying the words "CLEARED TO [location]" (7110.65 4–2–1b). The location they say is the clearance limit. If a pilot hears "CLEARED TO" they should know that they are receiving IFR separation (from both aircraft and terrain) and it is legal for them to enter clouds and other areas of reduced visibility.
ATC can also "clear" aircraft to execute an instrument approach procedure. This clearance does NOT change the flight rules status of the aircraft: IFR aircraft remain IFR and VFR aircraft remain VFR. If a VFR pilot receives an instrument approach clearance they still must comply with the applicable cloud clearance, ceiling, and visibility requirements which govern VFR flight. When initiating vectors to a practice instrument approach, ATC will specifically tell the pilot to "Maintain VFR" (7110.65 4–8–11a5), as a reminder that "even though ATC is providing IFR‐type instructions, the pilot is responsible for compliance with the applicable parts of the CFR governing VFR flight."
What separation services are provided?
Modified IFR separation.
When ATC "clears" a VFR aircraft for an instrument approach, they must provide modified IFR separation to the aircraft beginning "at the point where the approach clearance becomes effective" (4–8–11a2). "Modified IFR separation" means that the aircraft is provided any applicable separation as outlined in the rest of the .65: runway separation, lateral separation, non-radar separation, radar separation, visual separation, or vertical separation. The only exception is that, instead of requiring 1000' vertical separation between most other IFR aircraft, the minimum is 500'. (1000' is still required if either aircraft is a heavy or super.) For an IFR aircraft, an approach clearance automatically includes authorization to fly the published missed approach; this is not true for a VFR aircraft, which must receive prior authorization in order to be provided separation services when flying the missed (4–8–9).
What if ATC issues an "approval" only?
No separation services are provided.
If ATC does not "clear" a VFR aircraft for a practice approach, they must make this very explicit: "(Aircraft identification) MAINTAIN VFR, PRACTICE APPROACH APPROVED, NO SEPARATION SERVICES PROVIDED" (4–8–11a3). The aircraft may have been talking to ATC, may have been given vectors on to final approach course, and may even still be talking to ATC (if they are going in to a towered airport)—but no separation services are provided.
Why will ATC do one or the other?
Whether ATC issues a "clearance" or "approval" is prescribed the 7210.3 paragraphs 10–4–5 (for Terminal facilities) and 6–4–4 (for Enroute facilities). VFR pilots can expect to receive modified IFR separation when conducting practice approaches at the "primary airport" of an approach control, and at secondary airports "to the extent possible within existing resources." A Letter to Airmen should be published describing the type of services provided at a given airport, if any are.