Those aren't bad definitions from a lay perspective.
People get into trouble with "socialism" as "state owns the means of production" vs "social democracy" as "state provides pensions, benefits to the poor and sick, etc." Even in the latter case you can have differences such as in "socialized medicine" where, in the UK, the government owns the hospitals but in the US, Medicaid and Medicare cut checks to private hospitals.
Also one could claim that "Communist" governments have shown "Capitalist" characteristics in practice. Stalin's greatest accomplishment was starving the countryside to fund rapid accumulation of capital in the industrial sector. Brutal, but they survived Germany's onslaught in WWII. People in countries like India and China respected Stalin long after he was deprecated in the Soviet Union because they were hoping to develop as quickly.
Then there is contemporary China which has caused a political crisis in the west not because it is a "Worker's Paradise" but it seems so much more effective at capital accumulation. (e.g. they have high speed trains in Beijing, it costs us billions and billions to run one from Fresno to Bakersfield. They make EVs people want to buy, we make XXXL EVs that pile up in dealer lots unsold because nobody can afford them, etc.)
People get into trouble with "socialism" as "state owns the means of production" vs "social democracy" as "state provides pensions, benefits to the poor and sick, etc." Even in the latter case you can have differences such as in "socialized medicine" where, in the UK, the government owns the hospitals but in the US, Medicaid and Medicare cut checks to private hospitals.
Also one could claim that "Communist" governments have shown "Capitalist" characteristics in practice. Stalin's greatest accomplishment was starving the countryside to fund rapid accumulation of capital in the industrial sector. Brutal, but they survived Germany's onslaught in WWII. People in countries like India and China respected Stalin long after he was deprecated in the Soviet Union because they were hoping to develop as quickly.
Then there is contemporary China which has caused a political crisis in the west not because it is a "Worker's Paradise" but it seems so much more effective at capital accumulation. (e.g. they have high speed trains in Beijing, it costs us billions and billions to run one from Fresno to Bakersfield. They make EVs people want to buy, we make XXXL EVs that pile up in dealer lots unsold because nobody can afford them, etc.)