Does 'full' mean 'crowded'?
- "Full" means that something is at capacity.
- "Crowded" means "filled with many or too many people or things".
For example, a theatre might have a capacity of 300 seats. If all 300 seats are occupied you might say that "the theatre is full". You might not necessarily say that it is "crowded", as this implies over-capacity. The capacity of many indoor venues is set at a sensible level, often to safety standards. "Crowded" is defined as "leaving little or no room for movement", which simply would not be allowed in a safe environment.
In your example where it is speaking about "the streets" being "full of people", there are likely no imposed restrictions as to how many people can be there. However, as a native English speaker, I would interpret "the streets are full of people" to mean that they are busy, not necessarily "crowded".
That said, "crowded" can be a subjective word. Some people do not like crowds, and what one person considers to be "too many people" may be quite acceptable to another.
All things considered, I still feel that "busy" is more synonymous with "full" in this context.