"Resting state" is basically the state of not doing any specified task and not seeing any experimental stimuli. This is in contrast to most neuroscience experiments where the participant perceives stimuli or responds to them.
"Spontaneous activity" (also sometimes called "intrinsic activity") is the brain's activity which is not related to external factors/stimuli or to responses to them. When the participant is at resting-state, all of the activity you see using neuroimaging is "spontaneous activity". This term is also sometimes used during experimental tasks where you can separate activity that is related to the stimuli from "background" activity which is not related to the stimuli, and is therefore spontaneous/intrinsic.
The "default mode network" is a specific set of brain regions (usually including the angular gyrus, posterior cingulate cortex/precuneus, and medial prefrontal cortex) which have coordinated activity during both resting-state and task performance. This network is thought to deal with introspection, memory and other "inner" processes, in contrast to other regions responding to the environment and what happens in it. So when giving a stimulus to a subject that he/she has to respond to, the default-mode network will usually be less active, compared to during the resting-state. The default-mode network is one of the so-called "resting-state networks", along with many other sets of different regions (the visual network, the sensorimotor network, the dorsal attention network, and others).
"Resting state" is basically the state of not doing any specified task and not seeing any experimental stimuli. This is in contrast to most neuroscience experiments where the participant perceives stimuli or responds to them.
"Spontaneous activity" (also sometimes called "intrinsic activity") is the brain's activity which is not related to external factors/stimuli or to responses to them. When the participant is at resting-state, all of the activity you see using neuroimaging is "spontaneous activity". This term is also sometimes used during experimental tasks where you can separate activity that is related to the stimuli from "background" activity which is not related to the stimuli, and is therefore spontaneous/intrinsic.
The "default mode network" is a specific set of brain regions (usually including the angular gyrus, posterior cingulate cortex/precuneus, and medial prefrontal cortex) which have coordinated activity during both resting-state and task performance. This network is thought to deal with introspection, memory and other "inner" processes, in contrast to other regions responding to the environment and what happens in it. So when giving a stimulus to a subject that he/she has to respond to, the default-mode network will usually be less active, compared to during the resting-state. The default-mode network is one of the so-called "resting-state networks", along with many other sets of different regions (the visual network, the sensorimotor network, the dorsal attention network, and others).