You may have noticed that we can happily replace semicolons by a full stop, or vice versa, and it still makes sense. The meaning does change, however!
Let's try using a comma instead of the semicolon in the previous example:
Gareth slept soundly. Isobel was crying, this was quite rare.
There is nothing technically wrong with either statement. Now try full stops:
Gareth slept soundly. Isobel was crying. This was quite rare.
Again, technically the statement is correct, although what is rare is now ambiguous.