Your Translation Memory and Glossary tab has two separate lists:
Active Resources are the translation memories that you have assigned to the project you are creating or working on; MyMemory, the public translation memory shared by all Matecat users, is ranked first among the active resources and is indicated with a world icon. When clicking on the corresponding Import TMX button, users can add their TMs to the Public Memory.
By adding a resource, users ensure that all translations are saved in their private resources and not in the public memory. By default, any added resource has the Update checkbox selected; in this case the public translation memory will not be fed with the translated segments. In other words, users can choose not to have their translations saved in the public translation memory (MyMemory) by selecting the Update checkbox corresponding to the private key.
Inactive Resources are the translation memories that you have saved in your profile on Matecat. You can activate a TM and add it to a project by selecting the Enable checkbox next to the private key. Once the resource has been enabled, Matecat will automatically check both the Lookup and Update checkboxes. Users can manually clear the Update checkbox next to the private TM if they would like their translations to be saved inside the public translation memory.
Lookup and Update
For any TM, you can decide whether you want to use it to look up translation matches or to also save your translations to it. To do that, select one or both of the Lookup and Update checkboxes.
Only Lookup selected: the translation memory is only used to look up translation matches from your private TM;
Only Update selected: the translation memory is only used to save your translated segments in the private TM;
Both Lookup and Update selected: the translation memory is used both to look up translation matches and to save your translated segments in the private TM.