There is „zerówka”, but since „zerówki” are part of kindergartens(„przedszkola”) no one really differentiates them, other than legal context(child can skip kindergarten altogether since it's just a convenience for working parents, but „zerówka” is part of „obowiazek szkolny” and can't be easily skipped).
They may be different things in US, but according to Wikipedia it is treated the same for most of the world.
This optional year you're referring to is probably "zerówka" (grade 0). When I was a kid a bit less than 20 years ago, you would either have this year in kindergarten or in primary school, depending on the parents' choice. Now it got pretty complicated so I don't really know what's the current situation.
In the U.S.A., pre-school is optional and not part of free public education, ages 1-4. Kindergarten, however, ages 5-6, is mandatory and provided free by the government. It's no wonder that my son was more educated at age 4 by a "Russian" pre-school than he was by age 6 after attending public school kindergarten.