No. There is a huge difference. Dips are much more effective than pushups and much more difficult than pushups. Anyway, there are a million and one ways of working out ways to do dips at home.
If you have a kitchen where the worktop meets at an internal right angle, you can use that but it can be a bit hard on your wrists.
A better solution is a balustrade handrail which has a similar internal right angle. You can vary your hand spacing too. Wide for more pec stress and narrower for more triceps emphasis.
Russ' idea of the chairs is fine but just watch out that you don't pull one of the chairs off balance and end up in a heap on the floor. Another good reason not to go to total failure!