Backing up multiple os from same device

[strawberrypoint]

So, I have a 2010 Macbook (the plain white one) that was running on Snow Leopard OS 10.6.8, it was running pretty slow, so I upgraded to Yosemite OS 10.10 the day it came out (purely by accident). This caused a sort of conniption fit on my computer, sooo I backed it up using time machine with a new 2tb hard drive and took it to an apple store and had them 'downgrade' me to Lion OS 10.7.5. My computer has been running so much smoother! I have been able to simply drag and drop stuff from the external hard drive just fine. Now I am starting med school and decided to get a new macbook that will last a little longer than my ancient one. Is there a way to back up my current Lion os and all its files onto the same external hard drive using time machine (simply because it is so easy) without erasing the other time machine already on there? I am curious because I did not pull all my files off of the first time machine file backed up from the Yosemite os. I was wondering if I need to 1.) go back and put all the files drag and drop style onto the computer from the Yosemite time machine file and then time machine it again (because I will have everything off of there, and therefore will not care if it obliterates the old one), or 2.) if I should just drag and drop all files I have created/added since the downgrade to Lion os instead of using time machine, or finally, 3.) time machine will simply integrate all the new files into the old time machine even though I did not put all the files back on (I've sort of been using it as more of a holding tank until I need those certain files rather than sole a back up....), I don't really care about which os is on the time machine file, but I do not want to loose all my files that are on the old one. I'm not very computer savvy and would so appreciate the advice! Thanks!

 

[pigoo3]

"Wall of text". Please use paragraphs, bullet points, etc. for easier readability.

Thanks,

- Nick

 

[ManoaHi]

So, I have a 2010 Macbook (the plain white one) that was running on Snow Leopard OS 10.6.8, it was running pretty slow, so I upgraded to Yosemite OS 10.10 the day it came out (purely by accident) ...but I do not want to loose all my files that are on the old one. I'm not very computer savvy and would so appreciate the advice! Thanks!

Let me see if I have this correct in my mind:
1. you have a 2010 MacBook that was on Snow Leopard
2. it was upgraded to Yosemite, however, it is now running Lion
3. you have a TimeMachine backup while it was under Yosemite, but not Lion.
4. you have not yet bought a new MacBook (to be clear there is no new MacBook at the moment), so are you referring to the MacBook Pro or the MacBook Air?
5. on the 2TB external disk, which you have a Yosemite TimeMachine backup, you want to put a Lion TimeMachine backup on that as well.

If you are getting a new Mac, I don't really see the need for having the Lion MacBook TimeMachine back up. I'm thinking (correct me if I'm wrong), that you want to migrate some files from that backup (Lion MacBook) to your new Mac. If that is the case, just create a folder on the 2TB TimeMachine disk, and put the files (particularly the ones you thought you might lose) in there that you want to copy/move to the new Mac. That would be the safest. TimeMachine just makes it more tedious. If you absolutely want a Lion TimeMachine backup, I'd suggest getting another disk.

And as Nick said, please use bullet points. It is hard to follow your question. I may have completely misunderstood your question.