Pushing a domain name in the sense, pushing it to the auction winner, such as auctions held on ebay. However, you cannot push a domain name until it has been registered at the same domain registrar where the auction winner has an account. Whereas, Transferring a domain name simply means that you have to transfer the domain name to the another registrar. Pushing a domain name is absolutely free and registering requires to pay the fees.

For me there is no difference ... or just like the difference between a car and an automobile.

there is no such difference, for me its just the synonymous.

i think they are same and nothing is different.

The term push domain name is commonly found in eBay. Since domain names are just digital constructions, they cannot be shipped like other goods. They can only be pushed to the auction winner within the same registrar company (for it to be pushed to another person the original owner and that person must have an account with the same registrar company.) On the other hand the transfer of a domain name can be carried between different registrar companies

Well when you are referring to pushing a domain, it means that domain is transferred between the user domain control panels. This term is used when this transfer happens under the same registrar.For example, if a domain is registered under eNom's registry and a user A sells it someone named 'B' whose registrar is eNom as well, then the domain needs to be pushed from the user A's domain control panel to user B's domain control panel. Whereas when you speak about transferring a domain, that means the domain name is trasferred from one registrar to the other. Example: YOu have registered a domain with eNom but wish to switch to GoDaddy, in that case you need to transfer the domain between these two registrars.

I hope this clears the doubt.