Q:

Can charging by conduction and charging by induction occur simultaneously?

If I connect a neutral body to a charged body (suppose it is negatively charged) with a conducting wire, how will the neutral body get charged - by induction or by conduction?

A:

"Electrically charging an object" can have different meanings:

adding or removing charge from an object, i.e. changing its state so that the total charge is different than before by adding/removing electrons/ions. To do that, you need some way of conducting the charges (usually a wire for electrons). In your example, a wire could lead the electrons from a negatively charged body to a neutral body (assuming that both bodies themselves conduct sufficiently).
moving charges (i.e. changing the charge distribution) within the object without changing the total charge. In most cases, this includes performing work on the system and includes "charging a battery" = changing the electrochemical configuration. It can be done in any number of ways by creating an electrical or magnetic field, which leads to charge movement. This is governed by the Maxwell equations, which includes induction (applying force on electrons by changing the magnetic field).

Those phenomena can happen simultaneously if the setup is chosen accordingly. In your example, assuming conducting bodies, the charging will mostly be the done by adding charge. Additionally, the arising currents change rapidly and also create changing magnetic and electrical fields that perform work on the bodies, thus moving charge within the bodies.
I'm Austrian, so I can only say that the latter meaning is colloquial in German, maybe it's the same in English.

