Cuddle and snuggle are two affectionate actions which depict very similar meaning. These two terms are often used interchangeably for each other as they are very synonymous with meaning. Only to a degree of extent will you be able to draw out the difference between them. Both cuddling and snuggling have to do with showing a gender or warm affection by drawing close or lying close to each other.
This is often done between two lovers. These two actions are usually done while sitting together on the chair or lying together in bed. Talking about modern English, cuddling is considered to be of more intimacy than snuggling. When you snuggle, you may just make some manual movements towards your partner (be it human or pet), and it does not necessarily include the usage of your hands.
Cuddling, on the other hand, has to do with getting very close to your partner and also putting your hands or hands into actions probably by holding.