re: "is this lens for distance vision"
What distance a lens focuses at depends on the patient, not just the power of the lens. We can't tell from the power you gave us what distance it would focus best at in your case. The lens you received is a monofocal, and in the vast majority of cases if the lens is set for the best possible distance vision, you won't be able to read without reading glasses. A tiny minority of patients can, but given that it sounds like your distance vision isn't good, it sounds like the lens power left you myopic, nearsighted. The lens is likely focused at near or intermediate rather than at distance.
It is true that during the first few weeks the lens can shift position while it is healing in your eye, which changes the distance it focuses at, so it is possible your distance vision might improve some (and your near vision would get worse). Usually they wait until 3-4 weeks after surgery, or in rare cases 2-3 months, for the vision to stabilize before they prescribe glasses/contacts. If you don't wish to wear correction for distance vision, they could consider laser surgery or a 2nd lens implant to correct it.
Doctors estimate the lens power needed based on various eye measurements, but unfortunately there is no exact formula, it is just an educated guess based on statistics from prior patients. For most people it works well, but for some the lens power can be off.