Category, tags, author and so on are all "archives" sections in WP.
How these sections are displayed is based on the template file used by your template.
I didn't look at the photocrati theme but if you look at the template hierarchy in WP you will surely understand :
For your tag section, your theme can use tag.php, if this file does not exist, it wil use archive.php, and if this file does not exist neither, it will use index.php...
So look in your theme and try to find wich file is used.
In this file, you'll have a loop to display the posts.
In your loop, you have two choice to display the post :
<?php the_content(); ?> : to display the whole content of a post.
<?php the_excerpt(); ?> : to display only an excerpt. This excerpt can be generated by Worpdpress (the first 55 words) or you can write something in the optional excerpt when you write a post.
So, in your loop, just find wich tag is used and change it to fit your own needs.
You can change this tag in any template file. If you want only excerpt on your home page, again, find wich file is used in the template hierarchy (it can be home.php or index.php) and edit the loop.
Note that the automatic excerpt generated by wordpress will strip all the images and formatting (bold, italic, links, etc). But if you use the optional excerpt when you write a post, all the formatting in this field will be displayed.