Services, both in Distributed Environment and in Single Computer System's Memory can be either Stateful or Stateless.
a Stateless Service does not change it's state between handling 'requests' from 'Service Clients'. 'Response' depends only on the 'Current Request', not on 'previous operations' in that a Service.
a Stateful Service may change it's state between handling 'requests' from 'Service Clients'. 'Response' depends, and is determined by the 'Current Request' as well as on 'previous operations' in that a Service.
Previous operations might be internal operations, not triggered by requests (not very elegant solution to use such) as well as 'previous requests' from 'Service Clients'.
in a better case of better System's Design, only 'previous requests' from Service Clients are 'previous operations'.
Generally, Stateless services are more reliable, cheaper, faster, more secure and more easily duplicated to provide reserve components. Stateless services should be preferred wherever it is possible and not unreasonable. There are 'elegant solutions' that use Stateful Services however.
Stitie Machines (in Stitie Space or not; within a Single Computer System or in the Internet), can provide capabilities of either Stateless Services or Stateful Services.