You might be saying to yourself right now, "I didn't know there was a difference." If that's the case, you're not alone. The average person cannot tell you the difference between an escort card and a place card, but it's really quite simple.
When you walk into an event and you see a table with tented cards or small envelopes lined up, those are escort cards. They have a guest's name and a table number (or name) on them and their purpose is to "escort" you to your table.
Once you've arrived at your table, if there is another personalized card at each place setting, that is a place card. It tells you your "place" at the table.
It's very common at weddings these days to only use escort cards and allow the guests to arrange themselves at the table. Very formal events continue to use both escort and place cards, but if you want to save yourself a little time and trouble (and money on stationery and calligraphy!), just use escort cards.