Two good answers already, although I don't think either of them answer the question particularly clearly.
Do these two approaches accomplish the same thing?
Yes (if you're just talking about getting the website working)
Ultimately, both end up with an A record (as you can tell from the other answers, a type of DNS record) for your website pointing to your host's web server, which results in your website being accessible from your domain name.
Version 1) You configure your domain settings at the registrar to point to your host's DNS servers
This hands control of DNS for the domain to the host; the host's DNS servers will already be set up with all of the records you need (eg, A records) for your domain so you don't need to worry about setting up individual records. www.yourdomain.com will point to your website, ftp.youdomain.com will probably point to the address for ftp, the mail will already be set up etc.
Version 2) You use your registrars DNS servers, and configure an A record pointing to your host's web server
This leaves control of DNS for the domain with your registrar, you have to set up any DNS records yourself. They've given you the details for the record to set up the website, but you may also want to set up records for FTP and mail - this is main difference you'll see between the two approaches.