Correct, with one receiver both TVs will view the same show.
If your receiver has composite output - 3 RCA jacks - you can buy an inexpensive converter to coax, connect the BR TV to OTA jack and channel 4 or the one specified by the converter and you'll have SD viewing in the bedroom. Their might be a converter for component to coax also.
Or you can use HDMI over coax converters and HDMI splitter.
Or wireless HDMI converters and a HDMI splitter.
Or you can run a HDMI cable to the BR TV and use a HDMI splitter.
Or a second receiver for the BR TV and now the TVs can watch different channels.
