Several factors influence the decision about whether to have your webshop hosted by a different firm from the one you use to register and manage your domain names:
How much technical expertise and capacity you have
If your webshop is hosted by a different firm from the one that manages your domain name's registration (i.e. if your hoster is not your registrar), you will need to know a little about 'zone files'. Zones files are part of the internet's addressing system. Although they are hidden away 'under the hood', internet users rely on the information in them to reach websites, get their mail delivered and so on. Things won't work properly if the zone file doesn't reflect the actual configuration of your domain, once the website is on a server that isn't managed by your registrar. Do you have the expertise to handle that yourself, or someone to handle it for you?
How many domain names you have and what they are used for
If you have only one or two domain names, there's not much to be gained from using a registrar that isn't your hosting service provider. For convenience alone, it's probably best to have everything under one roof.
The situation can be different if you have a lot of domain names, especially if the sites and services linked to them are different. You might, for example, have a couple of domain names linked to popular webshops, plus some others that are used only for e-mail or simple, low-traffic sites. The best hosting firm for your webshops may be one that provides relatively expensive dedicated hosting services, while a budget service provider can host the simple sites. Administering your domain names (handling renewals, etc) will nevertheless be easier if all of them are with a single registrar. Using several hosters but only one registrar will inevitably mean separating the hosting from the registration services, at least for some of your domains.
Whether your preferred hoster supports DNSSEC
There are lots of reasons for wanting to use a particular hosting firm: service quality, support, familiarity, location, price, etc. But what if that firm doesn't support the security extension DNSSEC? You'd like the added peace of mind, but you'd prefer not to leave your old hosting firm. The answer may be to have your domain names managed by a registrar that does support DNSSEC, while leaving the hosting to your preferred service provider.
Whether you anticipate switching hosters
A reputable hosting service provider will always cooperate if you choose to take your business elsewhere. Sometimes, however, things don't work out as they should. Administrative complications, technical issues or a dispute with your hosting firm can occasionally make switching difficult or slow. Having your domain name registered through a separate registrar means that problems like that can never affect the continuity of your webshop.
... and, finally
There's one factor that should have no influence on your decision: price. Firms that concentrate on hosting often charge a little more for registering and managing a domain name. However, the difference is normally trifling in absolute terms. It won't affect your budget unless you have a very large number of domain names. Whereas the indirect cost of choosing the wrong service provider can be considerable.