Interline agreement means airlines will check baggage through. If two airlines do not have an interline agreement then have to pick up baggage at end of one airline and re-check baggage again for second airline. If you have two separate ticket, then when checking in at CTS the check baggage allowance rule of domestic CST-NRT JAL Express flight will apply. When all your flights are on one ticket then your international baggage allowance will apply for CST-NRT segment. But this tends to depend on check-in agent at the airport, how strictly they will enforce that.

Another situation with having two separate tickets is that SQ is not technically responsible at all if you miss SQ11 at NRT due to your JL CTS-NRT flight got delayed. If all flights are on one ticket then SQ will rebook you on next available flight. Again, if you are on two separate ticket then you have to rely on mercy of SQ agent at NRT if you missed SQ11 at NRT. Remember, strictly speaking by the rule SQ has no responsibility to accommodate you on alternate flight if you are on two separate ticket.