Fluorescence and radioactivity are two completely different things.
Fluorescence usually refers to a material that emits light (or "glows") when exposed to UV light. Radioactivity is a separate process where a material undergoes radioactive decay. Fluorescence is a chemical property and radioactivity is a property of the nucleus.
Many different minerals used in glass production are fluorescent, but it happens that when uranium dioxide is used in glassware, it is both fluorescent and radioactive. There is a lot of glass that looks like uranium glass, but only uranium glass will fluoresce with a distinctive green glow. Other materials may cause fluorescence, but only uranium will have the distinctive green glow.
For examples of uranium glass that fluoresce, you can do an internet search on "vaseline glass".
Also note that uranium was also used in pottery production to give distinctive yellow/red coloring. In this case, the pottery is radioactive, but not fluorescent.
In your comment, you mentioned that you were worried that the pigment may become airborne. If it is uranium glass, the uranium is safely sealed within the glass and you do not have to worry about it coming out. The glass will be slightly more radioactive than background radiation, but not enough to be a concern. Glass vitrification is actually one way they are considering how to dispose of and seal radioactive waste for millions of years.