Dezso,

I am not aware of a distinction between the two.  Perhaps the more important distinction is between voluntary and involuntary thoughts. One can choose to focus attention inward, but I think most researchers are more interested in unintentional mind wandering.

Mark Scerbo

There are also types of depression-related thinking that could be considered forms of mind-wandering.  For example, rumination involves repeatedly dwelling on a problem or event, and trying to suppress unwanted thoughts has the paradoxical effect of making them even stronger.

Personally, I think daydreaming is under conscious control while mind wandering is unconscious or preconscious. You don't tend to realise your mind has been wandering until you are interrupted, but you do have more awareness of daydreaming. Also you tend to control your daydream but you have less control over mind wandering.

I suspect that both terms might well describe the functioning of the default mode network encompassing the posterior parietal and posterior prefrontal which is operative all the time except when the task oriented network is activated.

As far as I know, daydreaming is just a type of mind-wandering. We spend most of our waking lives in a mind-wandering like state, dominated by automatic associative thinking and high activation of the Default Mode Network. Sometimes this thinking is directed inward, autobiographically toward the past or the future (which I guess might be what we think of as daydreaming), and sometimes it's directed outward, experienced as automatic judgments and associations between external stimuli and memories.

There subjective similarities between the dream and the mind wandering areas such as sensory, emotional, fantastic, mnemonic, motivational and social, besides the absence of cognitive and metacognitive control. Despite the aspects mentioned are present in both neural states, there are clear differences in prevalence, such as the emotional aspect and the fantastic which are more common, more immersive and more intense in dreams. These differences, however, are used to demonstrate that even the dream can be an enhancer species mind wandering since each difference of one particular aspect has a higher preponderance in dreams.

Don't get caught in a word game. It's rarely useful to try to map contemporary science onto classes of cognitive process that were assigned name centuries ago - that includes... consciousness, dreaming, attention, and certainly mindwandering and daydreaming. 

McVay and Kane's papers may be useful to you:

https://scholar.google.co.uk/scholar?q=JC+McVay+&btnG=&hl=en&as_sdt=0%2C5

Also try the following searches on PubMed Central:

http://www.ncbi.nlm.nih.gov/pmc/?term=daydreaming

http://www.ncbi.nlm.nih.gov/pmc/?term=mind+wandering

A daunting number of open-source research articles and reviews here!

The following has several chapters (by various authors) of broader relevance:

Handbook of Individual Differences in Cognition

Attention, Memory, and Executive Control

Editors: Aleksandra Gruszka, Gerald Matthews, Blazej Szymura

Thank you!