They seem behaviorally similar. Is the difference cognitive perhaps?
As he said, the difference between laziness and avolition primarily come from the causes of each behavior. Laziness is common among psychologically "normal" individuals while avolition is commonly seen in patients with schizophrenia or depression. Now I will go in depth with each to better characterize them and hopefully show the differences between the two. I will talk about avolition first because it is better defined in the field of psychology.
Definition of avolition mainly comes from research of schizophrenia symptoms. Schizophrenia symptoms can be divided as positive and negative symptoms. Negative symptoms can be divided into diminished expression and amotivation. Amotivation consists of anhedonia and avolition (Foussias & Remington, 2008). Anhedonia is diminished capacity to experience pleasant emotions. Avolition is the loss of drive and lack of curiosity. Avolition occurs in depression as well but is different for the two disorders. Avolition comes with saddening or depressed effect for people with depression, but this is not the case for people with schizophrenia.
Since activation of prefrontal cortex is generally associated with initiation of spontaneous activity (which is less in frequency in people with avolition), hypoactivation of prefrontal cortex may be the cause of avolition in patients with schizophrenia (Sebanz & Prinz, 2006). Another study shows anti-correlation between dorsal caudate activity and negative symptoms of schizophrenia including avolition (Mucci et al., 2015). This indicates that avolition may be caused by abnormalities in the motivation-related circuit. There are two networks known to be involved in motivation-related brain network: first one includes the ventral striatum, orbito-frontal cortex (OFC), insula, and medial prefrontal cortex (mPFC) and is involved in liking, reward anticipation, reward valuation, and representation of stimulus-reward associations. The other circuit includes the dorsal caudate and the dorsolateral prefrontal cortex (DLPFC), and is involved in representation of the expected reward and causal connection between action and reward (Liljeholm et al., 2011). Thus, there is a theory that patients with schizophrenia may exhibit avolition because they are not able to anticipate reward from their actions.
Laziness itself is not studied extensively in psychology primarily because it has not been well-defined. At first glance, laziness seems to be a familiar concept to the usual people. However, laziness may involve many factors of human behavior that are at times but not always exhibited in people considered to be lazy. For example, one of the requirements of being lazy may be having no motivation. Without motivation, the person is less likely to show desire to take certain actions. But plenty show desire and motivation; these motivations are just not targetted to a long term goal. With these difficulties in mind, I personally believe that one of the economics definitions of laziness is most in line with what people commonly refer to as laziness: tendency for people to focus on the activities that give immediate pleasure rather than longer-term activities (Frédéric Bastiat, 1850). Bastiat called it idleness rather than laziness, but I believe they are synonymous in this context.
For the cause of laziness, I must confess this is not something I am familiar with. However, popular sources such as this one state that there can be multiple causes for laziness. One would be lack of interest in the field itself. Another would be lacking faith that the action will be worth the effort - which is similar concept to learned helplessness. One study states that anterior frontomedian cortex is involved in making these internal judgements leading to decision making (Zysset et al., 2002). However, studies such as this does not show what causes change in the activation of the anterior frontomedian cortex.
I also noticed that a popular YouTube video about laziness refers to a mouse study that selectively bred physically active mice which led to physically active mice descendents having the same characteristics. The video uses this study to state that there are genetic factors involved in laziness. Not only is it a stretch to make a connection between laziness of humans and tendency to wheel run by mice, the study itself is flawed in that the mice were bred with their parents for the first few weeks. This means that environmental factors cannot be ruled out. Here's the paper if you want to take a look.
Bastiat, Frédéric. Economic Harmonies. George B. de Huszar, trans. and W. Hayden Boyers, ed. 1996. Library of Economics and Liberty. Retrieved May 29, 2016 from the World Wide Web: http://www.econlib.org/library/Bastiat/basHar20.html
Foussias, G., & Remington, G. (2010). Negative Symptoms in Schizophrenia: Avolition and Occam’s Razor. Schizophrenia Bulletin, 36(2), 359–369. http://doi.org/10.1093/schbul/sbn094
Leon F Seltzer (2008). Laziness: Fact or Fiction?. https://www.psychologytoday.com/blog/evolution-the-self/200806/laziness-fact-or-fiction
Liljeholm, M., Tricomi, E., O’Doherty, J. P., & Balleine, B. W. (2011). Neural correlates of instrumental contingency learning: Differential effects of action-reward conjunction and disjunction. The Journal of Neuroscience, 31(7), 2474–2480. http://doi.org/10.1523/JNEUROSCI.3354-10.2011
Mucci, A., Dima, D., Soricelli, A., Volpe, U., Bucci, P., Frangou, S., … Maj, M. (2015). Is avolition in schizophrenia associated with a deficit of dorsal caudate activity? A functional magnetic resonance imaging study during reward anticipation and feedback. Psychological Medicine, 45(8), 1765–1778. http://doi.org/10.1017/S0033291714002943
Sebanz, Natalie (Ed); Prinz, Wolfgang (Ed) Cambridge, MA, US: MIT Press Disorders of volition. (2006). vii 493 pp.
Stefan Zysset, Oswald Huber, Evelyn Ferstl, D.Yves von Cramon, The Anterior Frontomedian Cortex and Evaluative Judgment: An fMRI Study, NeuroImage, Volume 15, Issue 4, April 2002, Pages 983-991, ISSN 1053-8119, http://dx.doi.org/10.1006/nimg.2001.1008. (http://www.sciencedirect.com/science/article/pii/S1053811901910080)
Supposing that by "laziness" you just mean behaviours etc. apparently identical to avolition, then the difference is, assuming we call "avolition" a symptom of an illness, that avolition is out of the control of the sufferer, unlike laziness.
That's if we do agree that illness is out of a sufferers control, at least more so than their other behaviours. That is Fulford's 1989 attractive definition of illness:
failures of action that are beyond the abilities of a person
Naturalism in the Philosophy of Health, p72
Whether or not we call that "cognitive", as you ask in the question, may be less interesting than asking how we know that something is out of our control (presumably via introspection), and how it can be (presumably just biological if the mind is the brain).
Fulford, K. W. M. (1989). Moral theory and medical practice. Cambridge University Press.
Giroux, E. (2016). Naturalism in the Philosophy of Health: Issues and Implications. Switzerland: Springer International Publishing