A tart is a pie with a bottom crust and no top crust. What you're describing as an upside-down tart is a grunt. If you bake a grunt but serve it upside down, it's a slump.
There are also betties, crumbles, crisps, buckles, clafoutis, cobblers, crisps and pandowdies. Each is different, and some have regional disagreements.
Wikipedia suggests that a grunt is a type of cobbler [1]? Although [2] suggests its steamed?
[2] also suggests a slump is yet another cobbler variation.
The upside down tarts are what they try to pass off as pies in British pubs, I wouldn't class them as pies, just like I wouldn't class a tart as a pie. British crumbles,cobblers et al don't tend to have pastry bottoms, so I wouldn't class those as pies either.
Shepherds, Cumberland and cottage pie...... Are the exception that proves the rule :)
There are also betties, crumbles, crisps, buckles, clafoutis, cobblers, crisps and pandowdies. Each is different, and some have regional disagreements.