can i have separate websites with subdomains?

Hi I am a little confused about this and I would appreciate if someone can help me understand

I have a website (fake names)
and I don't understand is this separate from SEO point of view from
can I have a totally different website like
which is fully separate from the cats example above or does this mean that the 2 of them will share all SEO and therefore get it all confused between cats and sofas for search engines?

I know I can buy different domains, but I just want to understand this because if it is possible I want to avoid buying more domains.

Thank you very much for explaining!

Hi Kikos,

From my understanding of Sub-domains, G00gle treats sub-domains as totally different sites for seo purposes. I have 100's of sub-domains that are on completely separate topics and have their own set of on-site & off-site seo going on. Some are PR 0's whilst some are PR 5's.

Sub domains do not normally share juice with the main site.... however recently I put my google anylitics code for my main site on all of my sub-domains and created xml site map file with all sub-domains on the main root and added/verified all sub-domains to my main anylitics account and my rankings went through the damn roof within a week!
I am guessing that maybe the link juice for all 200 sub-domains may have combined through googles eyes with all the changes I made... not 100% sure on all this but just thought I would mention my experience with subs

Google treats subdomains as entirely different domains. You can save your budget and use the subdomains. However, do keep in mind that subdomains aren't valued as good as top level domain and with subdomains, you might not get desired results even with maximum SEO efforts.