First, there is no similarity between morphology and configuration. Second, maybe you could specify in what context you need the words, so we can give you clear answers (for example, are you talking about astrophysics, anatomy or linguistics?) In general: morphology is the study of forms (shape of something) ; configuration is how things are positioned in a set. That's the simplest way I could put it. Luis's answer is comprehensive.

"Morphology" refers to the study of the 'form' (shape) and structure of INDIVIDUALS, be they forms of life, cells, tumors, linguistic units, the earth's surface, etc. "Configuration" refers to alternative dispositions of SETS of functionally separable elements of an organic whole, either resulting from deliberate human choices (the configuration of software programmes, the configuration of an organization or institution, the different options a customer usually has when he buys a car or a computer, etc.) or from possible states of systems, or processes occurring in them (e.g., the relative position of the planets at a given time) that are regulated by natural laws beyond human control. A configuration is a COMBINATION of (freely occurring) elements of a SET and typically has alternatives. Morphology, form, is a property of ONE individual, it is not combinatory, and it has no alternatives at the interval of time under consideration (although, forms may change through time, of course).

The -ology suffix indicates morphology is a field of study. Configuration is just a noun belonging to the family headed by the verb "configure". "I don't make decisions based on the configuration, or relative positions, of the planets."