I find AS1221 is both the upstream and the peer of AS13445 from ipinfo.io/AS13445. However, as far as I know, there is no upstream or downstream relationship when talking about peering. Is anything wrong with my understanding?
First: please keep in mind that this is just a representation/interpretation of routing relationships as generated by one specific website based on information they most likely derive from routing tables and public routing databases.
Since there's no clear description on how ipinfo.io decides this, we can only make some guesses. But for example, it could be the case that AS1221 is peering with AS13445 on IXPs (which would make it a peer), and also advertises prefixes received from AS13445 to other networks (which would make AS1221 an upstream).
Upstream and downstream aren't well defined terms in routing, as routing really doesn't have a direction. They are all a matter of perspective. Traffic can flow in any direction. Any prefix can be announced to anyone - they may not accept it.
In the path AS1-AS2-AS3, as seen from AS3, is AS1 up or down from AS2? If AS3 is a Tier-1 ISP (no transit), most people would say everything is downstream of AS3, but that requires you to know they're "tier 1". If AS3 peers with AS1 (and they can), which way is up/down, now? Who's the top of the pyramid? (no one. there never was a "top".)
(If we muddy things with "business logic", downstream are the people who pay me, and upstream are the people I pay. But you can't necessarily get that from a route table.)