For a Continuing Reservation, you will have to come down to the front desk to check out/in, and get new keys. It's always beneficial to make sure that when you check in, that the CM knows there is a continuing reservation. 99% of the time, it is pre-blocked so that you can stay in the same room, but there's always a time when the TA doesn't let the resort know. It should be noted that depending on the length of the first reservation, that the 2nd reservation will not show up in the computer until midway through your stay. The resorts can only see 4-8 days out, give or take.
As long as the reservations are notated properly, there shouldn't be a problem with staying in the same room. However, if you booked two different category rooms, you will have to change.