The component provides an interface with a single method.
The component implements another interface with a single method.
First things first.
By component do you mean a Component model component?
If so, there is a difference between an implemented interface and a provided interface even though they look the same on a diagram.
An implemented interface, created by a realisation link gives you the option to override (i.e. implement) the interface methods. However, if you create it using the "element parent" context menu item (ctl-I) you dont get the option to do the override and will have to do it manually (select component and press ctl-shift-O).
Either way you will end up with a component with methods in its own right. These should ... let me check... yes they do ... appear in an sd message Operations list.
Now "provided" interfaces on components seem to be a different kind of fish. I am still struggling to understand their use 2 years down the track. They seem to be some sort of conceptual level adornment to a component that (IMO) only has use in breaking down assemblies. They dont seem to add any feature to the associated component.

You can check out what I mean by creating a component diagram and "adding" interfaces to a sample component using all the different ways and types.
Then try
1) colouring the component, this will show you some od the strangeness.
2) double click the lollipops - see more strangeness
3) investigate ctl-shift-O
4) dragging the lollipops around the component.
5) adding your interface classes to the diagram and look at their relationships
6) making sense of it all and telling me!!!
hth
bruce