There is no difference, both mean the same thing. ^o^

Both forms, the infinitive 'to dance' and the gerund 'dancing' are used as a noun. They use it as an object noun where "she" is the subject and "loves" is verb. In this case they can both be used to say the same thing. However, the verb you use in front of the infinitive or gerund can change whether you the forms are interchangeable. For example: 'She stopped dancing.' 'She stopped to dance.' These two sentences mean completely different things. 'Would you care to dance?' 'Would you care dancing?' Here, the second sentence makes no sense whatsoever. You must be careful when using infinitives in place of gerunds or vice versa and ask yourself if the sentence makes sense with the verb you are using. Research groups of verbs that: 1) Can be used interchangeably with infinitives and gerunds. 2) Change the meaning of the sentence when interchanged. 3) Lose meaning when interchanged.

They may mean the same thing, or they may be different, depending on the context. "Anna loves to dance" definitely means that Anna herself dances, and she loves it. "Anna loves dancing" could mean the same thing. However, it could also mean that Anna loves the art or act of dancing; that is, she appreciates the art of dance, or enjoys watching people dance. This is because "dancing" can be used as a gerund (a verbal noun), which means "the art or act of dancing".