I googled American foods and decided to pick accurate but different names.

• Sausage in a bun is a hot dog. Its the name CMOT Dibbler gave them
• Club Sandwich is what Americans call a Chicken BLT

Your Sausage patty comment brings out a great example because you can place them in a bread roll/bap.

So you could technically call saussages in a bread roll a sausage roll (after all when you put bacon in, its called a bacon roll). However most people know a saussage roll as a saussage wrapped in savoury pastry. It’s a completely different dish.