Elasticsearch, the recommended backend for making your logs searchable, is a separate project from logstash. Logstash does come with a built in elasticsearch, designed to get people up and running very quickly, but if you are considering any serious use of elasticsearch you would set it up yourself as a standalone service.
Logstash does come with a simple web interface, and kibana is a slightly better but still simple interface being ported into logstash. Again this is geared towards getting people up and running quickly, and at the end of the day it's just a pretty curl wrapper for elasticsearch.
You can also use logstash without elasticsearch/kibana, which we do for a good bit of our logs. I think logstash intentionally blurs the lines of what it is or isn't so people don't get caught up in trying to figure out how to get it running. Give it a try and see for yourself exactly what it is or isn't.
Logstash does come with a simple web interface, and kibana is a slightly better but still simple interface being ported into logstash. Again this is geared towards getting people up and running quickly, and at the end of the day it's just a pretty curl wrapper for elasticsearch.
You can also use logstash without elasticsearch/kibana, which we do for a good bit of our logs. I think logstash intentionally blurs the lines of what it is or isn't so people don't get caught up in trying to figure out how to get it running. Give it a try and see for yourself exactly what it is or isn't.