"Reading glasses" and "computer glasses" get used interchangeably, but they're built for two different distances, and using the wrong one is a common reason people say reading glasses "don't work" at a desk.
Two different distances, two different lenses
A book or phone held for reading sits roughly 30–40 cm from your eyes — near distance. A laptop or monitor sits further out, at arm's length — intermediate distance. Reading glasses are calibrated for the near distance; put them on for a monitor and the screen sits just outside their focus range, which is why text can look soft or you find yourself leaning in. Computer glasses are built for that longer, in-between distance, and are usually paired with a lens that also filters some of the blue-violet light and glare a screen produces.
If you're at a screen most of the day
Office work that's mostly monitor-based is the clearest case for computer glasses over reading glasses, whether or not you need a prescription — they're available with zero power as well as ground to your prescription if you already wear one. Computer glasses are worth it any day you're spending more hours looking at a screen than at a page.
If you're a student splitting time between books, a laptop and your phone
This is the case with no single right answer — a lot of student reading happens across all three distances in one sitting. If most of your reading is still on paper or a phone held close, reading glasses are the closer match; if lectures and assignments mean hours on a laptop, computer glasses close that gap instead. There's no harm in owning both if your day genuinely splits between them.
What about just reading on your phone?
A phone is usually held closer than a laptop but not as close as a book — near enough that reading glasses generally cover it, though if you notice eye fatigue specifically from long phone sessions, that's the same intermediate-distance strain computer glasses are built to reduce.
Not sure which is right for your prescription specifically? Here's how to read the numbers on it, or browse reading glasses and computer glasses side by side.