Here are the similarities between Instagram Stories and Snapchat Stories, broken down nicely by TechCrunch [emphasis by me]:

• The Stories format laces the last 24-hours of 10-second-max photos and videos you’ve shared into a slideshow you can tap to fast-forward through
• Everything you post disappears after 1 day
• You shoot full-screen in the app or upload things from the last 24 hours of your camera roll (recently added to Snapchat with Memories)
• You adorn your photos with drawings, text, and emoji, and swipeable color filters
• You can save your individual Story slides before or after posting them
• Your followers voluntarily tap in to pull your Story and view it, instead of it being pushed into a single feed
• People can swipe up to reply to your Stories, which are delivered through Instagram Direct private messages
• You can see who’s viewed your Story

Here are the differences between the two:

• Instagram Stories appear in a row at the top of the main feed instead of on a separate screen like Snapchat and are sorted by who you interact with most, not purely reverse chronological like Snapchat
• Anyone you allow to follow you on Instagram can see your Instagram Stories though you can also block people, opposed to building a separate network on Snapchat
• You don’t have to be following someone to view their Instagram Stories, which can be viewed from their prolfile as long as they’re public
• You can swipe right or tap the Stories icon in the top left to open the Stories camera, opposed to Snapchat defaulting to the camera
• You can hold the screen to pause a slideshow, or tap the left side to go back a slide, oppose to Snapchat’s time-limited, constantly progressing Stories
• You can’t add old content [older than 24 hours] to Instagram Stories unless you reimport or screenshot, while Snapchat lets you share old Memories with a white border and timestamp around them
• Instagram offers three brush types for drawing: standard, translucent highlighter, and color-outlined neon, opposed to Snapchat’s single brush
• Instagram offers custom color control for drawing with an easy picker as well as pre-made palettes like earth-tones or greyscale, while Snapchat custom color control is much more clumsy
• Instagram currently lacks location filters, native selfie lens filters, stickers, 3D stickers, and speed effects but you can save content from third-party apps like Facebook-owned MSQRD and then share them
• You can’t see who screenshotted your Instagram Story, while Snapchat warns you
• You can’t save your whole day’s Story like on Snapchat, but you can post slides from your Story to the permanent Instagram feed

The emphasized parts are my favorite changes/additions.

I personally love the idea that Instagram now allows for more raw footage like Snapchat, but you still have a little wiggle room to curate. So it might not be 100% raw, but it definitely lowers the standard of "Instagram-worthy" to encourage more sharing on Instagram.

I can see myself using Instagram Stories a lot and then later promoting that one "highlight" shot of the day to my traditional Instagram timeline. It just seems like such a natural and seamless workflow.

Cheers to stealing like an artist but making it your own.