You can share a SharePoint Online site (or a list or document, etc.) with external users, if your global setting for the site collection allows this. Although you need to select a specific permission group for these external users (from the list of available permission groups in that site), those external user do not have the same capabilities as a ‘normal’ user of the site.
The reason for this is that external users do not have an Office 365 license linked to them, at least not unless you choose to assign that to them.
As a result there are a number of things you cannot do as an external user. Microsoft has some documentation on those limitations:
I recently found that there is at least one other thing that external users cannot do, which is not documented: An external user cannot share something with another external user by inviting them.
On the one hand that makes sense, because that could potentially allow an endless string of external users in the site. On the other hand it is strange: if I am allowed into the site as an important user with broad permissions, then why can’t I share anything with another (new) external user?
What I haven’t tried yet is to see if an external user can share with new external users once an Office 365 / SharePoint Online license is assigned to his account. Will update this post if I find out.