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A soft fork creates an altcoin too, by branching the chain (that is why it is called a "fork").

An altcoin is created whenever there is a change to the protocol that changes the definition of which blocks are valid (the 'consensus rules'), whether by restricting it, extending it, or both, after a certain block.  

Whether the change is a strict extension or a strict restriction, as soon as someone mines and broadcasts a block BL[n] that is valid under version L of the protocol (the more liberal one) but invalid under version R (the more restrictive one),  the miners running version R will ignore it and mine their own block BR[n].  Thereafter the miners running version R will only try to extend their branch, because the other one includes a block that they consider invalid; whereas those running version L will mine on top of whichever chain is longest.  

If the L miners are a majority, so that their branch grows faster than the other, they will eventually mine on their branch only, while the R miners will only mine on theirs.   The coin will effectively have split.  Sooner or later, two conflicting transactions (spending the same coins to different addresses) will be included, one in each chain, and then the split then  will become manifest.

If the L miners  are a minority, they will see many or all of their blocks orphaned, and presumably would then switch to the R version for self-interest.