Why aren't Tugboats called Pushboats?

J'Amazen and I had a great paddle on Lyttelton Harbour today. Starting off from Cass Bay we slogged into an unrelenting noreaster for 1.5 hours, by which time we should have been almost half as far again. So, we decided that that was enough and stopped for lunch at Gollans Bay! The weather brightened up after that and we enjoyed our paddle back with a dropping tail wind - shame about that!

We'd seen this container ship plowing its way up the harbour, accompanied by two insignificant little tug boats and were intrigued to see them pushing this mighty big ship into the wharf. Why aren't they called push boats? And if the tug boats were insignificant we were probably under the radar with our little kayaks and kept well out of the way!