Yes. Shove is much harder and more aggressive than push. For example you push a door open and that is a normal, everyday activity. But if you shove a door open that is very aggressive and angry and the person would have done it with a lot of force. Also there is a phrase in English involving these two verbs and it is: When push comes to shove... (insert thing that needs to be done) If something can be done "if push comes to shove", it can be done if the situation becomes so bad that you have to do it. Suggesting that if you are forced to do something (i.e. you are "shoved") then you will do it but if you are encouraged to do something but it is not necessary then you are only being "pushed" and that is not as hard as shove. However this is only metaphorical, you cannot interchange "force" and "shove", only in this phrase. Hope that helps!

Yes, 'push' is the neutral, general term, while 'shove' is more specific. 'Shove' (which rhymes with 'love', pronounced with an 'u' sound) is both a verb and noun. A shove is a quick, rough and careless movement. 'Shove' can also simply mean 'put'. For example: 'What should I do with the dishes?' 'Oh, just shove them in the sink. We can wash them later'.

The are synonyms, they have similar meanings, but are used in different contexts. Push can also be used in the IT world. It is also more polite. Good luck with your English!