Both connect() and bind() system calls \'associate\' the socket file descriptor to an address (typically an ip/port combination). Their prototypes
I think it would help your comprehension if you think of connect() and listen() as counterparts, rather than connect() and bind(). The reason for this is that you can call or omit bind() before either, although it's rarely a good idea to call it before connect(), or not to call it before listen().
If it helps to think in terms of servers and clients, it is listen() which is the hallmark of the former, and connect() the latter. bind() can be found - or not found - on either.
If we assume our server and client are on different machines, it becomes easier to understand the various functions.
bind() acts locally, which is to say it binds the end of the connection on the machine on which it is called, to the requested address and assigns the requested port to you. It does that irrespective of whether that machine will be a client or a server. connect() initiates a connection to a server, which is to say it connects to the requested address and port on the server, from a client. That server will almost certainly have called bind() prior to listen(), in order for you to be able to know on which address and port to connect to it with using connect().
If you don't call bind(), a port and address will be implicitly assigned and bound on the local machine for you when you call either connect() (client) or listen() (server). However, that's a side effect of both, not their purpose. A port assigned in this manner is ephemeral.
An important point here is that the client does not need to be bound, because clients connect to servers, and so the server will know the address and port of the client even though you are using an ephemeral port, rather than binding to something specific. On the other hand, although the server could call listen() without calling bind(), in that scenario they would need to discover their assigned ephemeral port, and communicate that to any client that it wants to connect to it.
I assume as you mention connect() you're interested in TCP, but this also carries over to UDP, where not calling bind() before the first sendto() (UDP is connection-less) also causes a port and address to be implicitly assigned and bound. One function you cannot call without binding is recvfrom(), which will return an error, because without an assigned port and bound address, there is nothing to receive from (or too much, depending on how you interpret the absence of a binding).