The bathroom mould is most probably one of the Cladosporium species although there is a possibility it could be one of about seven closely related moulds. Much closer examination would be required to give you a precise answer.
Cladosporium is one of the most harmless mould species found indoors ironically because we are all exposed to it in one way or another - it is the most common mould species found in air samples. All the same, in sensitive individuals, it can lead to allergy and sometimes, asthma.
If the mould you see in the washing machine compartment looks identical to the one in the bathroom, its probably also Cladosporium although some can only be told apart under a microscope.
The Fungi Kingdom is divided into five divisions and Cladosporium is amongst a division called the Ascomycota. However, any fungal organism may loosely be referred to as a "fungal growth", so yes, in this case in very simple terms, the terms are interchangeable.
Look up Cladosporium on Google Images if you want to compare the appearance of your mould with other identified samples.
Finally, for those with a fondness for referring to Wikipedia as a source of information, be very wary of the comments under "Clinical Information". Much of it is simply not true and appears to have been taken from something called a "Health and Energy" website in a cited link. The company appears to be a health pressure group of some sort : 'nuf said.