In the two tense English verb the shift between proximate verb form (love) and remote verb form (loved) operates on four bases

time - present/past

probabilty - likely/unlikely

psychological distance - informal/formal

and direct / reported speech

that binary structure then combines with two aspects (progressive and perfect)

and various modals (will/would etc) and other verbals ('had better' etc)

Advebs provide a lot of the temporal information because 3 of the four factors on which the proximate/remote structure operates are non-temporal