I see these terms used interchangeably, and I actually wanna stick to one. Which of the two is better and why? Which sees more common usage?
blog entry and blog post is not the same.
Blog Entry is generic "entering content in your web appplication being a weblog"
Blog Post implicates a specific taxonomy (see wikipedia taxonomy)
e.g. this could also be:
depending on the blog system you use.
In e.g. WordPress there is a taxonomy for objects like pages and posts and the option to add a lot more objects (custom post types) and a taxonomy for taxonomies like tags and hierarchies and the option to add a lot more. So the more this trend evolves the more "blog entry" and "blog post" will diverge until it is not clear anymore that you mean with "blog entry" a "blog post".
If you were my customer and would ask I want a blog system for making entries, I would not completely understand and ask more. If you would say "I want a blog system for making blog posts" i would be clear.
Good example here: http://wordpress.stackexchange.com/search?q=custom+post+types
If you say "I'm going to make an entry in my blog" you are generically speaking. You are going to put some content in your blog. And because we know of the history of weblog systems we all assume that you are referring to a blog post (with a certain date, a title, some content and possible some tags and hierarchies attached). If you say "I'm going to write a blog post" you are very specific of the type of object you are entering in that system and much more exacter.
Historically blog systems started as smaller applications (I wrote my own around 2000) with only one purpose but as functionality grew also the architecture behind it. So also the model behind it. Which led to more than only "posts" as objects being managed by such systems. Many blog systems are growing to be more and more CMS like systems. Look e.g. at WordPress. This trend will continue.
As you said, these two terms are used interchangeably and they have the same meaning. As to the usage frequency, Google search results show that "blog entry" is more common.
"blog entry": 339.000.000 results
"blog entries": 288.000.000 results
I think you can also call it just a post, instead of blog post that is why it is found more often blog entry in google. I would say that post is the most common way to say it.