as a Swinley / Crowthorne regular I've yet to really work out where one starts and the other finishes tbh. I think technically the permit is for the Crown Estate area hence you don't strictly need one for only Crowthorne Woods, but given I'm not exactly sure where one starts and the other finishes it's probably better to get a permit anyway (for £2, what's the issue)
There's pretty similar stuff in both although the slightly more technical stuff is generally over towards the Surrey Hill area (although Corkscrew is in Crowthorne)
Map on the Gorrick site is quite useful http://www.gorrick.com/downloads/swinleyforestmap.pdf
There's very little which is absolutely off limits, the army land is fenced off and flagged obviously, and there's Caeser's Camp to the north end which is also off limits for its archeological significance, plus occasionally there's eg: foresting or nesting bird areas which are temporarily off limits but they will be clearly marked. Or indeed, areas for wizarding antics.