There are differences between the various restrictions/bans in Dark Souls Remastered and we've included some additional details below:

Disconnecting from a multiplayer session(s) (in-game restriction):

Players that disconnect from multiplayer sessions repeatedly (either intentionally or accidentally) will have an in-game restriction placed on their account. This in-game restriction will remain until the player can maintain a stable online connection while playing in multiplayer sessions. This is intended to make sure that the online experience remains stable for all players online. There is no clear information on how long a player must maintain a stable online connection while playing the game in "Online" mode, but it is generally around 10 - 15 hours (or longer) depending on the frequency and severity of the disconnections.

Violations of the End User License Agreement (for using cheats, hacks, mods, or other similar external tools regardless of the reason or justification):

Restricted: Will generally not receive any messaging since the account/profile will still be able to play with the online multiplayer aspects, but will have restrictions placed on their account to limit their online interactions. These types of restrictions will usually be time-based and provided the player removes any mods, hacks, or cheats and proceeds to play legitimately, they will have their restrictions lifted once the time has been reached or the files in violation of the EULA have been completely removed. 

Banned: Will have a message that is displayed the moment the game is launched and the game attempts to log into the Dark Souls Servers which will block all access to the online multiplayer aspects. These types of restrictions are reserved for players that, depending on the severity of the violation, have violated the End User License Agreement (EULA) to the point that their profile/account is completely blocked from access to the online servers. This will also be the outcome of any players that had previously been restricted, had their restrictions lifted, but then proceeded to violate the EULA instead of playing legitimately. Please note that banned accounts/profiles are permanent and WILL NOT be lifted.

*Please note that there is currently a message that pops up when the game is launched and found under the "information" section to inform players that should they choose to violate the EULA, that restrictions (temporary or permanent) may be placed on their account. This message DOES NOT mean that restrictions or bans have been placed (and is only meant as a warning to inform "all" players of the consequences for any such violations).

**Additionally, for end users playing on the Steam/PC platform that are receiving the error message "Failed to Retrieve Data" this can potentially mean that restrictions have been placed on their profiles/accounts and would recommend contacting their region's support team for any additional information.

Is there a way to request restrictions be lifted?

If this is the first time your profile/account has been restricted, end users can contact the specific support team for their region (NA, EU, Asia, etc.) to request the account/profile be checked by the Dark Souls Server team. Depending on the severity of the EULA violations, end users can request their account be checked to see if the restrictions may have been lifted. Again, whether or not the restrictions will be lifted is ultimately the decision of the Dark Souls Server team and their decisions will be based on the severity of the EULA violation(s).

*Some players have notified us that restrictions were placed on their account due to a hacker/cheater invading their world and hitting them with status effects or items that could potentially flag their account as violating the EULA (these are mostly rumors, and provided the player deletes their save shortly after having this happen, should not result in any such restrictions/bans being placed on their account). As a precaution, it is recommended that players create a backup of their save data before playing Dark Souls Remastered in Online mode to counter any such issues until these players that are violating the EULA can be properly blocked or expunged from the online servers.