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I would like to know the difference in meaning, approach and concept between:

Clustering similar objects into more than one cluster (soft clustering) where objects can be found in more than one cluster, and soft classification where objects can be labeled into more than one class.

For clustering I would like to cluster my data into predefined clusters by used K-means and for classification also there are predefined classes.

In other words:

cluster 1 for example combine ( object 1 , obejct 2 ..etc ) 
cluster 2 for example combine ( object 1 , obejct 5 ..etc ) 
and 
Class A = for example assign to ( object 1,object 4, etc. )
Class b = for example assign to ( object 1,object 7, etc. )
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See the papers:

Peters et al., 2013, where authors compared $k$-means to fuzzy $c$-means and rough $k$-means as important representatives of soft clustering.

Jain et al., 2003, where authors examined the performance of fuzzy rule generation methods.

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Clustering is unsupervised learning. So you don't have the predefined clusters, these clusters are learned by the clustering method. Classification is supervised and you have to predefine classes. That is the difference.

Their results may look similar, but the input/output/objective are different.

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