Why do my iMessages (green bubble) don't appear on my iPad 2? but only on my iPhone I have what appears to be the same iMessages on my iPhone 6 and iPad, 2nd generation. Yet, when someone writes me a message, it only appears on my iPhone and not my iPad (although I have a whole list of names who I have already corresponded with on my iPad).

If I receive it on my iPhone, why do I not get it on my iPad? And why can't I compose a new message from my iPad (the send button it greyed out).

It's a lot easier for me to respond with my iPad because it has a keyboard and some people prefer to send me messages on my iMessage against my messenger.

I went to Settings and they correspond to each other.
The iMessage app on iPhone can send both an iMessage message as well as a regular SMS. An iMessage is shown as a blue bubble, while an SMS as a green bubble.

Assuming you are signed into both your iPhone 6 and iPad 2nd generation, you can receive and reply to SMS (green bubble) from your iPad (as well as other Mac and iOS devices signed in using the same Apple ID), by using a feature called Text Message Forwarding. The option can be found by going to Settings apps → Messages → Text Message Forwarding and turning on the switch which appears against your iPad device in the list.

For step by step instructions, you can go through the Apple Support articles, Use Continuity to connect your Mac, iPhone, iPad, iPod touch, and Apple Watch and How to forward SMS/MMS texts on your iPhone.

The messages in the cloud feature also might be worth enabling if you care to have your messages sync status by checking in with iCloud as opposed to relying on every device being online all the time.