As a PP indicated a READING (Near) prescription is used for hand held items: phone, book, mail, documents, food packaging etc
An intermediate is used for items about arm's length: laptop, desktop, worktop, tills etc
Your old reading glasses are now your intermediate prescription and your new reading prescription is ok for hand held range but not arms length range.
To put that into numbers as an example:
Old reading prescription +1.50
New reading prescription +2.25
New intermediate prescription +1.50 (same as old reading prescription)
Multifocals combining and distance/intermediate/near prescriptions didn't work out for you. That's ok, not everyone tolerates them. The optician remade them as your new reading prescription but that doesn't work for the range of your computer but your old glasses do.
Welcome to multiple pairs of glasses of varying strength dotted round the house depending on what activity you need them for. Sewing, crafting, diy, mending, painting, housework/cleaning, workshop, gardening, eating your dinner, dials on the cooker/washing machine, looking at the satnav. The list is endless!