socket file descriptors are the same among different processes

I have a simple server-client program. When I invoke the clients in separate ./client calls, each client is assigned a different file descriptor for its connection to server. But when I call them through the following bash script, all clients get the same socket fd:

for i in {1..5}
do
  ./client &
done

Here's my code:

client.cpp

int main (int argc, char *argv[]) {
    int sockfd;
    std::string ip = "127.0.0.1";
    char temp_char;

    establish_tcp_connection(ip.c_str(), 45678, &sockfd);
    printf("Client connected to server on sock %d", sockfd);

    // make sure that the socket is not closed before other clients start
    // so, just send a dummy char back and forth
    sock_sync_data (sockfd, 1, "W", &temp_char);    

    return 0;
}

Server.cpp

int main (int argc, char *argv[]) {
    int CLIENTS_CNT = 2;
    int server_sockfd;
    char temp_char;
    int sockfd[CLIENTS_CNT];

    struct sockaddr_in serv_addr, returned_addr;
    socklen_t len = sizeof(returned_addr);

    server_sockfd = socket (AF_INET, SOCK_STREAM, 0);

    memset(&serv_addr, 0, sizeof(serv_addr));
    serv_addr.sin_family = AF_INET;
    serv_addr.sin_addr.s_addr = INADDR_ANY;
    serv_addr.sin_port = htons(45678);

    bind(server_sockfd, (struct sockaddr *) &serv_addr, sizeof(serv_addr));
    listen (server_sockfd, CLIENTS_CNT);

    for (int c = 0; c < CLIENTS_CNT; c++){
        sockfd[c] = accept (server_sockfd, (struct sockaddr *) &returned_addr, &len);
        printf("For client %d on sock %d", c, sockfd[c]);
    }

    for (int c = 0; c < CLIENTS_CNT; c++) {
        /* just send a dummy char back and forth */
        sock_sync_data (sockfd[c], 1, "W", &temp_char); 
    }

    close(server_sockfd);
}

And here's my util code:

int sock_connect (std::string servername, int port) {
    int sockfd, n;
    struct sockaddr_in serv_addr;
    struct hostent *server;

    sockfd = socket(AF_INET, SOCK_STREAM, 0);

    memset(&serv_addr, 0, sizeof(serv_addr));
    serv_addr.sin_family = AF_INET;
    serv_addr.sin_port = htons(port);
    serv_addr.sin_addr.s_addr = inet_addr((char*)servername.c_str());
    if (connect(sockfd,(struct sockaddr *) &serv_addr,sizeof(serv_addr)) LESS_THAN_SIGN 0){ 
        printf("ERROR connecting");
        return -1;
    }
    return sockfd;
}

int establish_tcp_connection(std::string remote_ip, int remote_port, int *sockfd) {
    *sockfd = sock_connect (remote_ip, remote_port);
    if (*sockfd < 0) {
        printf("failed to establish TCP connection to server ");
        return -1;
    }
    return 0;
}