When you have to deal with glass at home, the difference between tempered and regular is pretty real. Tempered glass goes through a heating and rapid cooling process that makes the surface way more resistant to impacts, blows, and temperature changes. If you smash something heavy against regular glass, it breaks straight into big, sharp shards - way too dangerous. Now tempered, when it breaks, it disintegrates into small rounded pieces that cause way less damage. It's like the difference between regular ceramics and a plate you drop from the sink and it stays in one piece.
Tempered really does have better resistance, but there are some details that matter for your situation. If the window is somewhere with a lot of impact (near a kitchen, an area with small kids, or on a lower floor), tempered is totally worth it for safety. The downside is you can't cut or drill tempered glass afterwards - you have to order it at the exact size. If your renovation is still in the measuring phase and you want flexibility, maybe regular works out cheaper right now, but it's risky.
Another thing: tempered handles heat from the sun and climate changes better without creating internal stress that cracks. In an apartment, especially if it gets direct sun all afternoon, that makes a difference. If the glass shop is charging you a lot for tempered, it's worth getting a quote somewhere else - it might just be the standard for the type of window you want. Overall, if the price difference doesn't break the bank, tempered is the smarter investment.