Is it only to provide the correlation between the image and the object? What is the difference between the correlation via entanglement and classical correlation?
You are right. Ghost imaging has been proven to work also with the classical - thermal light. In such case, strong classical correlations between intensities of light are needed. See paper attached, where the authors directly study the problem you are addressing. As they say in the conclusion, the only benefit of using entanglement is the higher visibility.
You might be also interested in our recent paper on new imaging technique relying on holography that uses quantum interference between single photons, see attached link.
http://arxiv.org/pdf/1509.02890v1.pdf
Article Ghost Imaging with Thermal Light: Comparing Entanglement and...
When considering ghost imaging ones needs to distinguish systems in which the correlations apply to the average over many photons or at the level of individual photon pairs. In the many photon case (perhaps when a beam splitter is used to create two copies of the same random intensity distribution) then most of the main results of ghost imaging can still be achieved -- see work of Gatti et al. and Boyd et al.
However, beams splitters can't make copies of single photons. A very convenient way of making two photons with the same position is parametric down-conversion. Although such sources are entangled, for ghost imaging one only needs correlation in position (c.f. EPR type experiments when you need to be able to show both). So one can do ghost imaging based upon position correlation alone and in this situation it is a use of entanglement NOT a prove of it.
In relation to EPR one can also perform ghost imaging using the momentum anti-correlation between the photon pairs -- so in that sense switching between the two cases of position correlation and (from the same source) momentum anti-correlation one can demonstrate something corresponding to the EPR paradox. see
EPR-based ghost imaging using a single-photon-sensitive camera,