What is the different between Internet Investment and Offshore Investment?

Offshore Investment generally means you are investing via a broker or company that is based in a country other than your own and doesn't market its' services directly in your country. For example, a US citizen might set up an account with a European bank, and through it be able to invest directly in stocks and/or funds that don't trade on US exchanges or can't solicit customers in US.

By internet investment I assume you mean investing via the internet (as opposed to, for example, investing in internet companies). If I am correct, there are many brokers that allow you to trade online (as opposed to calling a broker to execute trades). So in the context of your question, I believe you are referring to executing trades/transactions via the internet. Besides being in same country, a difference here vs. offshore investment is also most likely ease of making transactions - very easy via Internet, whereas if you are dealing with an offshore company you may have different restrictions on when and how to conduct trades, not to mention a likely time difference that narrows the window of time you are able to make transactions or talk to a representative during the day.