Three types of slime mould
There are actually three classes of slime moulds, all are classified in a group called the mycetozoa ('fungus-animals')
Protostelida are mostly microscopic with tiny fruiting bodies, they were only discovered in the 1960's and haven't been studied much as they're hard to find and very difficult to keep alive in the lab.
Dictyostelids live most of their lives as single celled amoebae but come together to form a structure called a slug (not related to actual slugs) or grex when they need to form spores. They're often kept in laboratories and often used as models for intercellular communication and cooperation.
The myxogastria are the 'acellular' slime moulds that we’re talking about on these web pages. They're not really acellular ('without cells') - they're single celled - 'unicellular'. They form single giant cells that look like a network of veins and can cover square metres of ground in some cases.