Do iMessages (blue) or text (green) simply latch on to previous message?

Hello, I am very new to any type of cell phones - let alone iPhones - so please excuse me if this is kinda' dumb. I tried to search for this answer and the closest was done in 2010, so it was 'suggested' that I start a new conversation.

I have think I have managed to send myself (ie same iphone sends & receives it) an iMessage and a text (?SMS) to my husband's Android phone. Each time I thought that I was initiating a brand new message, but they seem to merely 'latch on' to the message that I had previously sent to either myself or my husband?

1. Am I doing something wrong since I don't seem to be able to start a brand new message?
2. If this is normal, how old can the original message be that you then link onto to? I mean something like if I send my husband a text one week and then another the following week, will they still be written 'together'? It seems like you could be texting about wildly different topics, yet they'd still be 'attached'??
3. And, can you print out these messages?

Thank you very much for any assistance!