It's not clear which of two possible things you mean by "IP address". You could mean the IP address as seen by your computer -- the one assigned to it. But you could also mean the publicly visible IP address, the one others see you connecting from.
The assigned IP address may be the same by pure coincidence. For example, many routers use 192.168.0.2 through 192.168.0.254 as the range they assign to clients. So there's always a chance you'll get the same IP address on two different networks.
However, those are internal, private IP addresses. When you connect out from most small networks, they use something called 'NAT' (Network Address Translation) to make your connections appear to the outside world to come from the router you're connected to. The router at Starbucks is not going to have the same public IP address at the router at your university (or data would have no way to tell which of those two places to go).
Computers have individual IP addresses, but they are typically assigned to them by the particular network they connect to.
You'll get a much simpler answer if you ask a more exact question. For example, when you say "will my ip address be different", it's not clear whether you mean your IP address as seen by your computer or as seen by the sites you connect to.