Namecheap and Cloudflare are both a registrar.

A registrar allows registering new and current domain names through their services. They have rules they must follow with ICANN, a US-based nonprofit Internet authority on assigned names (domain names) and numbers.

Depending on the Top-Level Domain (TLD) you want, different registrars may be necessary. Not all registrars allow registering any TLD. Namecheap has authority to act as a registrar for hundreds of TLDs, and they have been in business for decades. They are well trusted and well networked.

Cloudflare is also a registrar. They have TLDs they have authority to register names for as well like Namecheap. But Cloudflare is newer than Namecheap. They are both well established at this point. Your trust between them may vary or may be pretty equal depending how long you’ve been managing domain names on the Internet.

Since they’re both registrars, they also allow you to update the DNS records for domains you manage through them. When a domain is registered, it is managed through the registrar. The first stop another party or user/client will go to is the Nameserver (NS) records, you can find them as a laymen by doing a WHOIS query on the domain name. There’s typically two nameservers for redundancy but only one is needed to resolve records. These nameservers are then responsible for all of the other authoritative records you might expect, the A/AAAA/MX records and such.

So when you register a domain name and setup the nameservers differently than your registrar had default configured, you’re essentially keeping some authority at one service (Namecheap) and allowing another authority to manage the records (Cloudflare). Additionally, the origin registrar (Namecheap) will no longer permit managing DNS records as they point to a third party nameserver (Cloudflare), they will simply be the authority for the domain (maintain WHOIS records) and where you do renewals.

With Cloudflare managing the nameservers and by extension the DNS records, you have more flexibility than Namecheap. Cloudflare has a free CDN service and allows you to mask your server’s real IP address. They also have a large global network capable of handling DDoS attacks all with a click of a button from you to initially set it up and then automatic mitigation from there. Though it’s important to consider that the free Cloudflare services are limited since you’re not paying a premium, you certainly can but it can get expensive quickly and more than your domain costs per year, the CDN and free DDoS mitigation is for HTTP/HTTPS only, so if you have more complicated needs like a game server or other hosted app that requires simple A/AAAA records then you may not see the point of Cloudflare.

Help me understand something, DNS records are the info (A, AAAA, TXT, etc) that’s modified to configure services like websites and mail servers to a specific domain, right?

In a word, yes. These A, AAAA, MX, TXT, etc records are modified to configure services like websites, mail servers, and other services.

Their client will ask the configured authoritative nameservers for the record they’re requesting. If you go to “www.example.com” then it’s going to first lookup “example” in .com’s (a TLD) registry and then ask the nameservers at “example.com” for the A/AAAA record at “www.example.com” and hopefully get a reply with the IP address of the site.

An A record holds an address for IPv4 TCP/IP communication.

An AAAA record is identical to an A record in all respects except it is for IPv6 addressing.

An MX record declares which server(s) your domain’s email messages should be routed to.

A TXT record does nothing other than store text content as its value. It’s useful for some programs, but especially email, since it’s often used for the email SPF record which declares rules on how you would like to permit others to handle email on your domain’s behalf.

Anyway, hope this explainer helps, you seemed confused so I went detailed.