what are the trains from Hongkong to cities in Mainland China

Guangzhou and Shenzhen are connected with HK by train: At HK Hung Hom, you can take a train to Guangzhou East in around 2h; at the same station, take MTR East Rail line to Lo Wu and cross the immigration border to Luohu, Shenzhen. Of course, both of the cities can also be reached by coach.

What's more, there are many cities in mainland connected with HK by coach, such as Foshan, Shunde, Dongguan, Huizhou and Chaoyang.

From Hung Hom in Kowloon area, there are direct trains to reach Guangzhou East Railway Stations.
HK has many cross-border buses to reach many cities in Guangdong Province, such as the Foshan, Shunde, Guangzhou, Shenzhen, Dongguan, Kaiping and so on.

Thanks for info. In addition to the cities you mentioned
I would appreciate your guidance for travel from HK to Shanghai by train, and HK to Beijing by train