I just tried it on Perl 5.14, I do not get exactly the same thing with your two one-liners:

$ perl -MO=Terse -E'my $str = "McA"; $str = $str . " ";'
LISTOP (0x600153910) leave [1]
    OP (0x60007fdb0) enter
    COP (0x60006e3c0) nextstate
    BINOP (0x6001f1ea0) sassign
        SVOP (0x60006e2e0) const [3] PV (0x6001f2c08) "McA"
        OP (0x60006f890) padsv [1]
    COP (0x6001f7fe0) nextstate
    BINOP (0x6001f7fa0) concat [1]
        OP (0x600153980) padsv [1]
        SVOP (0x6001f7f60) const [4] PV (0x6001f2b78) " "
-e syntax OK

$ perl -MO=Terse -E'my $str = "McA"; $str .= " ";'
LISTOP (0x600153910) leave [1]
    OP (0x60007fdb0) enter
    COP (0x60006e3c0) nextstate
    BINOP (0x6001f1ea0) sassign
        SVOP (0x60006e2e0) const [3] PV (0x6001f2c08) "McA"
        OP (0x60006f890) padsv [1]
    COP (0x6001f7f60) nextstate
    BINOP (0x6001539c0) concat [2]
        OP (0x600153950) padsv [1]
        SVOP (0x600153980) const [4] PV (0x6001f2b78) " "
-e syntax OK
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There are some differences on the ante-penultimate and penultimate lines. But I am not really able to assess whether the difference is significant. The Deparse module also gives different output for these two lines in Perl 5.14.