They’re somewhat different. Mycroft is a more general purpose tool, snips appears to be more specific. Mycroft is open source, snips wasn’t last time I looked.
Mycroft can be run locally, though its default configuration doesn’t have that setup. You’ll need to run the personal backend service (https://github.com/MycroftAI/personal-backend). You’d also need to run deepspeech (https://github.com/mozilla/DeepSpeech) or kaldi or something else to do ASR/STT. You can run mimic (1) fairly easily, or if you’re looking for a more human-sounding voice, you can try mimic2 (https://github.com/MycroftAI/mimic2).