It's not the same unfortunately. The birth - 6 month ones are very tightly regulated, the 6-12 month ones aren't. They're suitable for children who are getting some of their nutrients from solid foods - so really the 6 month thing is not quite right these days. That dates from when it was advised to begin weaning at 3 months so solids formed the majority of the diet by 6 months. (In 1980 for example it was considered sufficient to change to cow's milk at 6 months).
These days we are advised to wean more slowly and solids should be supplementary to the main nutrition which is breastmilk or formula until solids begin to take over at approx 9-12 months.
NHS advice and first steps nutrition (which is an independent source of info for parents and health professionals about formula and baby foods) both recommend using first infant formula until 12 months. I used to think this as well - why stick with a non-discountable version if a cheaper one is available and suitable? But now I would stick with first stage unless the baby is pretty established on solids (at which point TBH cow's milk ought to be fine anyway). It makes sense to say for instance don't bother with the growing up milks for 12m+ because cow's milk (much cheaper, less sugar and you probably have it at home anyway) is fine, but it's harder to see the sense behind don't bother to switch from infant to follow on formula - when the switch is no bother for parents and may save money.
(But yes - better not to switch unless baby is having a good amount of solids)