On the Trenitalia website, for the date I want, it lists the departure times, then underneath "VE SL", and some have MESTRE beneath that in red, some just have MESTRE with no VE SL.

Our innkeeper advised that we should be leaving from S. Lucia, so I'm thinking that VE SL means the train originates at S Lucia and stops in Mestre (or the other way around). Is that right?

Grazie

You are correct.
Have fun !

ditto

All trains from SL stop in Mestre, but as you see the converse is not true.

If a train you wish to take only says Mestre, fear not. You can take a local shuttle train between the 2 stations. I believe they run every 10min or so, and take less than 10min.

Many thanks

SL is the station actually IN Venice. Mestre is a town on the mainland nearby. All trains from SL stop in Mestre-but not all trains to Mestre go on to Venice.