We used to call them "surprise bag" or "sweets bag", and they were a staple at
birthday parties - no one would dream of sending the young
guests off without one.
Unlike the UK variety, these were nostly home assembled (you could buy colourful little bags for them, though) and often contained home made cookies or came simply in clear sandwich bags.
The more homespun content, the naffer the bag - we all wanted everything store bought and brightly packaged...