This depends on how your modem router function is configured. Typically the devices connected to a modem get an internal local IP and the router funcion of the modem converts these to an external IP with port numbers that vary depending on the local IP's so that it knows which external packets belong to which internal local IP. The alternative is the router function of the modem assigns an external IP to the devices connected to the modem, essentially converting the in home lan into an extension of the internet. From what I've read, all cable modems can do this for at least 16 external ips, but the internet service providers limit this, for example my ISP only allows 3 external ips for a home account. The home dsl modems that do this typically provide 8 static external ip's but use 3 of these, allowing up to 5 connected devices to have independent external ip's. Note that one or more of those connected devices could be standard routers, which would be assigned external ip's and in turn assign local ip's to the devices connnected to the router.
Getting back to the original question, if the modem assigns external ips to devices connected to the modem, then the modem acts like a bridge and does not change packet ip information.
Side note, in the case of a cable modem, if it's disconnected from the coax cable (or the cable service isn't working), it then assigns local ip's, and the home network will behave as a lan. I don't know if a dsl modem does the same thing if disconnected from the phone line.