Bengali and Punjabi are ethnic groups.
The Bengali people are the ethnic community from Bengal (divided between Bangladesh and India) on the Indian subcontinent with a history dating back four millennia.
Bangla (বাংলা) is a a language of the eastern Indo-Aryan branch of the Indo-European languages spoken by the Bengalis. It is also a Malaysian derogatory term to refer to the immigrant workers originating from Bangladesh.
The Punjabi people (Punjabi: ਪੰਜਾਬੀ, پنجابی, also Panjabi people) are an Indo-Aryan ethnic group from South Asia. They originate from the Punjab region, which has been host to some of the oldest civilizations in the world including one of the world's first and oldest civilizations, The Indus Valley Civilization. There are also a number of Punjabi emigrant communities scattered around the world, especially in the United Kingdom, Canada, the United States, Kenya, Tanzania, Uganda, Persian Gulf countries, Hong Kong, Malaysia, Singapore, Australia and New Zealand.
The Punjabis speak Punjabi.
The Sikhs are the people who profess Sikhism. Sikhism is founded on the teachings of Nanak and nine successive gurus in fifteenth century Northern India, is the fifth-largest religion in the world. Most Sikhs live in the state of Punjab in India and, prior to the country's partition, millions of Sikhs lived in what is now known as the Punjab province of Pakistan.
Bayi is a Malay word for 'baby'. It is also a derogatory term referring to the Punjabis in Malaysia. Bayi Singh is a joke-provider and a Little Bird for Maverick of Cakap Tak Serupa Bikin blog.
[Correct me if I'm wrong] The Punjabis is Malaysia are often grouped as the 'Lain-lain' (Others) ethnicity. But since they were from India, they should be grouped as 'India' instead, if you insist not to refer all as 'Malaysians'.
The most prominent Punjabi is Malaysia is none other than DAP's Chairman Karpal Singh Ram Singh Deo. He and his sons are currently in a love-hate affair with Mahathir and his sons.
The Punjabis have their own political party - Parti Punjabi Malaysia, PPM.
OK. End of anthropology lessons.
Why all the fuss? This:
References from Wikipedia:
 Bengali people
 Punjabi people
Related reading: Ah OK-Lah Malaysian-Indian identity