No really, it's the same. The null operations are never seen by runtime perl and only exist in the optree as artifacts. I took the output from both of your lines, stripped out the null operations and they are 100% identical. Incidentally B::Concise provides better output than B::Terse.

$ perl -MO=Terse -e '$var = "String"; $var = "foo$var"'
LISTOP leave [1]
    OP enter
    COP nextstate
    BINOP sassign
        SVOP const PV "String"
        SVOP gvsv  GV *var
    COP nextstate
    BINOP sassign
        BINOP concat [1]
            SVOP const PV "foo"
            SVOP gvsv  GV *var
        SVOP gvsv  GV *var

$ perl -MO=Terse -e '$var = "String"; $var = "foo" . $var' 
LISTOP leave [1]
    OP enter
    COP nextstate
    BINOP sassign
        SVOP const PV "String"
        SVOP gvsv  GV *var
    COP nextstate
    BINOP sassign
        BINOP concat [1]
            SVOP const PV "foo"
            SVOP gvsv  GV *var
        SVOP gvsv  GV *var
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