Let's first take a look at their definitions:
Recycling is processing used materials (waste) into new products to prevent waste of potentially useful materials, reduce the consumption of fresh raw materials, reduce energy usage, reduce air pollution (from incineration) and water pollution (from landfilling) by reducing the need for "conventional" waste disposal, and lower greenhouse gas emissions as compared to virgin production. Recycling is a key component of modern waste reduction and is the third component of the "Reduce, Reuse, Recycle" waste hierarchy.
Upcycling is the process of converting waste materials or useless products into new materials or products of better quality or a higher environmental value.
To get a better feel of what the difference is please check out this article.