Persist and Press on

Persist verb - To continue despite difficulties, opposition, or discouragement.

Press on and persist are semantically related in persevere topic. In some cases you can use "Press on" instead a verb "Persist".

Press on verb - Continue moving forward.

Persist and press on are semantically related in proceed topic. You can use "Persist" instead a verb "Press on", if it concerns topics such as keep at.