After one minute of searching Google (i.e. not an expert),:

SL is a time-delay (slow blow?) fuse made for circuits with motors and solenoids. Likely something else is on that circuit like an air conditioner, refrigerator etc. Unless it was just stuck in there and an SL type was not needed. A fuse wouldn't blow from a light bulb so something else is going on which suggests maybe other stuff on that circuit. You might check to see what else is without power. An old house would not likely have a circuit with just one bulb and a 15A fuse.

D, I am not sure of but appears to also be a delay type.

http://www.cooperindustries.com/content/public/en/bussmann/consumer/products/home_circuit_protectionproductsandaccessories/fuses/plug_fuses_box_coverunits.html

Do they have the same screw base? If so, I think you are OK to use it.

The stamp on the bottom is probably the manufacturer.

If it fits, you can swap it. Fusestats were an attempt to keep people from putting oversized fuses in the panel. Originally, all the fuses were edison based (like a light bulb). Some one got the great idea of putting in a non-removable insert that would keep a 20A fuse, for example, from being screwed into a 15A circuit.

Fusetron is just Bussman's trademark for fuses.