Both 工厂 (gōng chǎng) and 工场 (gōng chǎng) are composed of the character 工, which means "work" or "labour". So they are similar each other and can be translated to "factory" or "workshop." However, the second characters 厂 and 场 make them different:
🔺工厂 is the most common term and means "factory" or "manufacturing plant". It refers to a building or group of buildings where goods are manufactured or assembled using machinery.
🔺工场 can refer to a "workshop" or "factory floor" where manual labor is involved, such as a craft workshop or a repair shop, often on a smaller scale than a factory.
In general, if you're referring to a large-scale industrial facility, 工厂 (gōng chǎng) might be a better choice, while if you're referring to a smaller-scale workshop or a place with manual labor, 工场 (gōng chǎng) might be more suitable. For example:
🔺这个城市既有众多的现代化工厂,也有许多历史悠久的各种工场。
🔺Zhè ge chéngshì jìyǒu zhòngduō de xiàndàihuà gōngchǎng, yě yǒu xǔduō lìshǐ yōujiǔ de gèzhǒng gōngchǎng.
🔺There are a lot of modern factories as well as various historical workshops.
(The city has many modern factories as well as various historical workshops.)