No, arbitrage is not the same as Forex trading, although they are related.
Forex trading: You buy and sell currencies to profit from changes in their prices. Example: You buy EUR/USD at a low price and sell when the price rises.
Arbitrage: You take advantage of a price difference for the same currency or asset in two different markets/brokers at nearly the same time, buying where it's cheaper and selling where it's more expensive.
So, forex is a type of trading market, while arbitrage is a strategy that can be used in Forex and other markets.