No. vassals and defensive pacts are entirely different things, but in game and historically. Sure there may be a bit of a grey area, but generally no.
Lets take WWII as a good example of everything (and when it was put into effect):
Poland, France, and the UK effectively had defensive pacts, so when Poland was attacked the other two were drawn into war.
British and French colonies (represented by vassals in game) were immediately into the war.
Vichy France is the same as if France capitulated to Germany.
German puppet states in Eastern Europe (and more obviously and famously Japanese Manchukuo) were in civ terms vassals. Permanent Alliances extend this relationship.
The biggest thing: defensive pact puts the two the partners on equal terms (sure one may benefit more than the other, but they both receive the same benefits).
Vassals is when there is a clear leader and follower. Where one tells the other what to do.