I was just wondering if there is any difference between supersecondary structure and motifs. As well, is a protein domain an independently folded region of a protein that has a particular function associated with it - that may or may not contain one or multiple motifs.
All supersecondary structures are motifs, but not all motifs are supersecondary structures.
Motifs, in a biological sense, are very similar to fashion motifs. They are patterns that repeat in a lot of different places. Supersecondary structures are motifs that are made of several secondary structures. Some motifs are much smaller (pockets for holding ions are 3-4 amino acids long), or involve no secondary structure interactions (see SLMs).
Regarding the second half of your question, a protein domain (depending on who you ask) is any region or regions of a protein that do something, regardless of how it is folded. Very often, domains can fold correctly on their own. Generally, the required protease/functional assay to determine whether a possible domain is really technically a domain is not usually done. For example, the kinase insert domain found in some tyrosine kinase receptors is considered a domain, despite being a) quite small b) unable to perform its function in isolation (not entirely fair, as its function is to phosphorylate the rest of the receptor).
In sum: protein domains have a couple of competing definitions, so you cannot assume that something referred to as a 'protein domain' is capable of performing its function when separated from the rest of the protein.
Domains can be of nearly any size (due to their functional and not structural classification), but very small and very large ones are rare. They can be made of any number of motifs, or none at all.
A few well-defined searches can quickly resolve questions like these:
1: is any difference between supersecondary structure and motifs?
Motifs and supersecondary structures are synonymous. src
2: is a protein domain an independently folded region of a protein that has a particular function associated with it? (that may or may not contain one or multiple motifs?)
"Each domain forms a compact three-dimensional structure and often can be independently stable and folded. Many proteins consist of several structural domains." Wiki: Structural Domain
"Several motifs pack together to form compact, local, semi-independent units called domains." Wiki: Protein Domain