Is a Beef Wellington a Pie?

Last night I had a Beef Wellington, at the Honest Lawyer Restaurant in Cockermouth.  It was made by putting a little filet mignon inside a puff pastry.  It was delicious.  I am not sure if this counts as a pie, but most pies I've been eating lately are basically beef and pastry crust, so I'm including it here on my pie blog.  I think most Beef Wellingtons are made with the whole tenderloin, not just a little filet, and if so, mine was like a pasty, or hand-pie, as some call them; an individualized little combination of beef and crust.  Very nice. 
In France, there is the filet de bœuf en croûte (fillet of beef in pastry), which seems to be a Beef Wellington here. 
Here are a couple photos of my Beef Wellington.