Type C or Type L adapter for Italy?

I have only used the C. https://www.worldstandards.eu/electricity/plug-voltage-by-country/

We have just used the C type that is sold in Rick's online store. Always take at least two as they are small and easily left behind.

Depends on what you are trying to plug in.

Are you plugging in 3 prong plugs? Then yes, L is the type. Otherwise for things like cell phones and other low powered electronics, the type C is all you need.

Mark has it right. Does the plug on your appliance have 2 pins or 3 pins?
If it is 2-pin, then 2-pin type C is OK.
If it is a 3-pin plug, you need a 3-pin type L plug (3 pins in a line).

Both types fit into an Italian socket. I have heard some newer Italian hotel rooms also have Schuko (type F) sockets to cater for visitors from northern Europe. Type C also fits in these.

If it is 2-pin, then 2-pin type C is OK.
If it is a 3-pin plug, you need a 3-pin type L plug (3 pins in a line).

Both types fit into an Italian socket.

This is what I thought at first, but the adapters we got from Amazon...the Type C will NOT plug in the Type L socket.

On all the Airbnb's we stayed at...they have both types, but the Type L is more prevalent on the rooms and the Type F sockets in the kitchen and bathroom areas.

I brought both Types C and L, so we were covered.

but the adapters we got from Amazon...the Type C will NOT plug in the Type L socket.

Then you got a badly designed adapter (plenty around), or a non-standard socket. The 2-pin type C (aka Europlug) has 4mm diameter pins, same as the 3-pins of a type L.
A Schuko plug (type F) has 4.8 mm pins. The idea is you can't put an earthed Schuko plug into an unearthed type C socket (though some people have been known to force it and break the socket), but you can but a (4 mm) type C Europlug in a (4.8 mm) Schuko socket.

Phone chargers sold in mainland Europe (including Italy) have type C Europlugs and fit in all these sockets.

Or maybe just buy a couple of USB devices that plug into Italian sockets. Cost about five euro.