Sometimes they say it fully, Senior, sometimes the short version.
Same goes to Jr. (junior): Neymar Jr. Or Neymar Junior, meaning Neymar, o filho.
They used it a lot to distinguis the actions that happened in the government of Bush Sr. (Bush o pai/Bush pai) from that of Bush Jr. (o filho).
To the wet-behind-the-ears learner it could be a kind of "false friend". He/she could confound Sr. with Senhor, especially the ones from Portuguese and Spanish speaking countries. With time one gets the hang of it, though.