I thought that they actually crossed the Sea of Reeds. The Red Sea designation was a bad interpretation that has persisted for centuries.
There happens to be a Red Sea, but there isn't any Reed Sea; also, it makes no sense that two words alike in the "into" language would be confused -- there's nothing to recommend the idea, IOW. It happens that the bitter lakes which are now somewhat freshened by the Suez Canal are in the correct general ballpark, but there's still not any apparent way for those to drown the Pharaoh. So, if it was a natural event, it isn't one that has taken place since then.
Had (for example) the escaping Hebrews just crossed the Nile before a large tidal surge rushed up from the Mediterranean (requiring of course some kind of mechanism for the tidal surge in the first place), it seems pretty likely that the Biblical account would say, it happened as the Pharaoh tried to cross the Nile.
The sea of reeds is a proffered notion by those who want a naturalistic (read dismissive) explanation to supplant the supernatural.. The crossing was at the red sea and markers were set at the crossing point by Solomon, one of which still stands today. The one on the Saudi side was removed...
I was taught about the Sea of Reeds too. But I've read more recent works that say that King James actually got it right and Red Sea is correct. So I don't know which is correct.
Typing mistake? It was the REED Sea and a scribe left out one of the "E"s . LOL Human error.