Fluorescent bulb went out. Went to a loal hardware store to get a replacement.
Original is Sylvania F18W/133 T8.
The replacement I bought looks similar, but the label is:
Sylvania F24 T8 CW, 18W 4100K, and the pins look slightly different. Where they meet the metal ends, the old one has a contact that rus the full diameter of the bulb, but on the new one, the contacts are just independent circles around each pin.

I replaced the bulb. it fits, but doesn't light up.

First, did I cheap out and I really do have to by exactly the same one for some mysterious (to me) reason?
Second, is there another part I should replace? My understanding is that sometimes the sockets go bad...but I don't know how to check for the problem. All other features of the hood are working fine.