"Socialism" is loosely defined as "social ownership and democratic control of the means of production."
That is more like the definition of "communism".
To me, socialism is more general term that contrasts to "capitalism", in the sense of bein more society-oriented rather than individual-oriented. Among other things:
(1) each individual should be rewarded by society in proportion to what he does for society, rather than by his possestions, descent, titles, intelligence, shrewdness, etc.;
"In a higher phase of communist society, [...] after labor has become not only a means of life but life's prime want; [...] only then can the narrow horizon of bourgeois right be crossed in its entirety and society inscribe on its banners: From each according to his ability, to each according to his needs!" --Marx
Socialism was presented as a transitional phase, Communism the ideal/logical outcome. A fairly murky distinction, depends on context and who you ask: Soviet Union was technically Communist and Socialist, Communist Party but CCCP -> USSR -> Union of Soviet
Socialist Republics
(2) property and economical rights of the individual are not absolute but are subordinate to the interests of society as a whole,
Identical in Communism and Socialism.
(3) the state is supposed to provide public services like health care, education, social security, transportation infrastructure, emergency and security services, etc.;
Ditto. Hard for not_state to provide those services when the state owns the means of production.
(4) the state should try to ensure equal opportunities to everybody and ensure that everybody has a decent minimal living conditions.
That's already happening in Communism. Remember, with no landlords, someone has to provide housing.
Socialism definitely does not imply state ownership of the means of production;
Not sure where you're getting that. Source?
but it implies state regulation, e.g. to force companies who provide vital services like water or electricity to charge reasonable prices, respect quality standards, provide basic service even to unprofitable areas, etc.. It admits, but does not require, that such services be provided directly by the state, by civil servants or through state-owned companies.
Socialism implies protection of consumer rights and mandatory product quality and safety standards; but is quite compatible with free market economy. In fact, as part of protecting consumer rights, socialism implies state intervention when needed to keep markets free, by preventing the formation of monopolies and cartels.
What you're describing is contemporary Capitalism, not Socialism. Socialism, as a minimum, is intrinsically consistent. What you're describing (privite ownership of the means of production") is difficult to reconcile with the Socialist ideal ("from each according to his ability, to each according to his needs").