Of course all characters that fail their save against the web are stuck in it.
Once a character saves against the web, how hard is it to leave the area?
A web is a 20-foot cube, and a grease is a 10-foot square, so we might get a situation like this:
. . . . . . . . . . w w w w . . . . w G G w . . . . w G @ w . . . . w w w w . . . . . . . . . .
so the character would need to move 5 feet to leave the grease and an additional 5 feet to leave the web.
Here are some relevant rules about being prone:
Standing up takes more effort; doing so costs an amount of movement equal to half your speed.
To move while prone, you must crawl or use magic such as teleportation. Every foot of movement while crawling costs 1 extra foot. Crawling 1 foot in difficult terrain, therefore, costs 3 feet of movement.
So, if a character is prone but unrestrained in the position above, one option would be to stand up (using 15 feet of movement) and then walk 5 feet over difficult terrain (using 10 feet of movement), ending in the web but not in the grease. The character would need a new save vs web on the next turn.
Another option would be to simply crawl out of the area, using 15 feet of movement to leave the web+grease square and an additional 10 feet of movement to leave the web square. The character would not need any more saves and could stand on their next turn, but attackers would have advantage against the character until they stood up.