Whit - This is a question that many have a hard time defining and fewer really understand. The easiest and most pedestrian way to take this is to explain it thusly:
Italian Renaissance is often referred to as being more feminine than Spanish Mediterranean. Structures tend to be more symmetrical and evoke European influences. There's a use of Classical order columns instead of Tuscan. There's more delicate detail and ornamentation on the exterior trim such as balustrades, windows, and doors. It's also common to see brackets supporting the overhang. Occasionally you'll also see brick facades. Spanish Mediterranean is less ornamental. It's crisper and more masculine. This style, also known as the Mizner style, was very popular in the 1920s when less ornamentation was in vogue. There's a lower pitch to the roofs and a heavier massing than Italian Renaissance. The Italian Renaissance has a more deliberately shaped massing, often into symmetrical expressions. The Spanish Mediterranean's massing is likely to be more haphazard and freeform.
Renaissance styles in America were most popular in the 1920s, so it is most likely not this style if it was not built during this period.