Clustering seems to be a 'strange' phenomenon. On one hand - clusters shall be made out of companies located in same / close areas. However, it is rather common that firms that form cluster are essentially apart. In case of the latter , rather the 'company`s profile' plays a role in clusters forming. 

The answer is "both". When will clustering happen? One way to sort this out is to consider the spatial differentiation. Starrett's spatial impossibility theorem deals with this. If you were to live on a plain with no special topological features, any location will do. There is no spatial competitive advantage. This condition falls into an a-spatial scenario. But once some "seed of attraction" is sown, like a farm or a factory, that seed will either die or grow into an industrial clustering and complex that will through time become more and more tied to its spatial ecology. Transport costs differentials and variations in rents for instance, start to incentivize strategic locations on that plain (and affects decisions related to production/residential sites) in a once featureless landscape. Therefore  to start clustering, you need seed it. There is a certain expectation which may be motivated by fundamentally a-spatial reasons (e.g. balanced development). But once it gets going and the concern is to nurture industry, space needs to be factored into the growth equation (very often it seems to be ignored but our very physical existence depends on it-  note that there are no industrial agglomeration on the web- there are virtual communities). If you think that history is NOT important than you will fall back on expectations. If you think that expectations are NOT important than you will fall back on history. Either approach has its merits/proponents and you will find that somewhere down the line one morphs into the other.

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It is a spatial cluster because of its make up

I think it is a question of definition. There are regional (see e.g. Enright) and industrial clusters. The first one is based on geographical concentration by definition (it can be called industrial districts, milieu, etc.). But for the second one it can be a very long distance  between firms. For example, aviation industrial cluster in Europe includes firms in France, GB, Spain, Germany, etc.; many machinery clusters in Russia have technological partners all over the country. In industrial cluster technological interaction is much more important than other forms, which can be essential in regional cluster (such as social interaction, labour interchange, knowledge diffusion, etc.).

I very agree with last opinion. I can add, that in our research driven in last 10 years in Polish Industry System, I see significant meaning this two different tracjectories in well- and low-developed countries. In first group, spatial proximity plays important role for innovation activity. For second group, more important is technological proximity. It seems, that in less-developed countries spatial and technology proximity work opposite way - closest means lack of knowledge. It's much different as in well-developed countries.

Cluster is ALWAYS spatial, i.e. it is connected to location, access, communication, power, etc. that are always spatial and spatially executing phenomena. Cluster often means that certain activities are located close to each other but clustering can take place also over longer distance (through networks). Also, all enterprises located close to each other are not necessarity connected to each other. However, spatial does not mean only geographically close or territorial. 

I agree with Shian-Loong Bernard Lew, and at the same time venture to say that there is a informational agglomeration in the virtual communities as well. If we search some information the agglomeration is demonstrated. Clustering in a sense also reduce the search cost of the customer, in addition to other benefits.  

Would you agree that the cluster concept has originated not so much as a spatial phenomenon of industrial conglomeration, but rather as a territorial (i.e. geographical) pattern of industrial networking?

One of the problems with management research is its very sloppy approach to terminology, so the same term means umpteen different things,  This is why the field is so non-rigorous and has limited impact on policy and corporate strategy.  In economics, clusters have a strong geographic connotation beginning with Marshall.  However, more recent literature in economic geography (e.g., Bathelt et al, 2004) recognizes that cluster potency depends not only internal resources and characteristics, but also linkages to other clusters.  Lorenzen and Mudambi (2013) extend this view, pointing to a typology of linkages (connectivity) and propose a model that implies systematic effects on local innovation. 

Many answers provide pieces of truth.

I think that it is more spatial phenomenon, since geographical coordinate of cluster exists. On the other hand, cluster can emerge in completely random place (like Silicon Valley, far away from large cities). There is randomness and path dependency (see Brian Arthur's book on path dependency, 1994, also with spatial examples) in the selection of particular location. Probably this is the reason of why some economists consider it as non-spatial phenomenon.

It might be useful to keep a distinction between clusters (as spatial phenomena) and sectoral systems of production and innovation [or simply: networks of firms] (as non-spatially organised entities). Otherwise we end up being confused - as we are now, suggested by the contributions above.

Yes...it is a spatial phenomenon, see

-Keith Head & et. al., (1995), Agglomeration benefits and location

choice: Evidence from Japanese manufacturing investments in the

United States, Journal of International Economics.