These are mostly introduced, alien, exotic, non-indigenous, or non-native species, or simply an introduction, is a species living outside its native distributional range. There is no difference between these two categories because invade and find new environment. 

What is the context? If there is any ambiguity, I think it is better to use alternative terms like exotic or introduced plants as suggested by Dr. Upadhyay. Some introduced plants get well acclimatized to a location and become native plants over time. Many food, ornamental, fruit, timber and other crops introduced in different countries have become almost native in respective countries due to their centuries of use.

This all depends in timelines. In Europe for example plants introduced from wherever prior to 1492 are often regarded as native, although they are technically pre-Columbian introductions, many of which have however been naturalized. Overall I would prefer "non-indigenous" species, simply for language reasons. Not all introductions are  invasive however. Also, an important aspect are local varieties - lots of crop plants have been introduced in many parts of the world, and have then been bred in distinct, local varieties. These are technically "non-native", but they are - as varieties - indigenous.

Both are same. Please see the below given link.

https://en.wikipedia.org/wiki/Introduced_species