This information is sent in an API-response the background when accessing the Marketing Cloud dashboard. So you can either check the network tab of your browser's developer tools or use the Google Chrome extension "Salesforce Marketing Cloud - Developer Tools".
Instance Info
If you open this extension and visit the Marketing Cloud Dashboard, basic information about the account and the currently logged in user is displayed. Furthermore the Marketing Cloud applications are shown along with the information if they are provisioned in this account and the current user is allowed to access them.
(Source: Salesforce Marketing Cloud - Developer Tools (Google Chrome Extension) - Product Website)
This is how the interface of the chrome extension displays the account type:
As this is just an intercepted API-answer, I can't ensure that this is always an appropriate answer. To have a definitive answer, you should look at the contract or get back to the account executive.
However, the values match the AccountTypeEnum values of the SOAP API. Using the following table (taken from AccountTypeEnum documentation) you can identify what edition this corresponds to:
| Name | Data Type | Description |
|--------------------|-------------|----------------------------------------------|
| BUSINESS_UNIT | Enumeration | Indicates a business unit account type |
| CHANNEL_CONNECT | Enumeration | Indicates a enterprise account type |
| CONNECT | Enumeration | Indicates an advanced account type |
| DOTO_MEMBER | Enumeration | Indicates an on-your-behalf account type |
| ENTERPRISE_2 | Enumeration | Indicates an enterprise 2.0 account type |
| EXACTTARGET | Enumeration | Indicates a core account type |
| LP_MEMBER | Enumeration | Indicates a lock-and-publish account type. |
| None | Enumeration | Default response type for AsyncResponseType. |
| PRO_CONNECT | Enumeration | Indicates a reseller account type |
| PRO_CONNECT_CLIENT | Enumeration | Indicates a reseller client account type |
You can also retrieve the AccountType-value via the SOAP-API:
<soapenv:Envelope xmlns:soapenv="http://schemas.xmlsoap.org/soap/envelope/" xmlns:xsd="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<soapenv:Header>
<wsse:Security soapenv:mustUnderstand="1" xmlns:wsse="http://docs.oasis-open.org/wss/2004/01/oasis-200401-wss-wssecurity-secext-1.0.xsd">
<wsse:UsernameToken wsu:Id="UsernameToken-24440876" xmlns:wsu="http://docs.oasis-open.org/wss/2004/01/oasis-200401-wss-wssecurity-utility-1.0.xsd">
<wsse:Username>ccc</wsse:Username>
<wsse:Password Type="http://docs.oasis-open.org/wss/2004/01/oasis-200401-wss-username-token-profile-1.0#PasswordText">ccc</wsse:Password>
</wsse:UsernameToken>
</wsse:Security>
</soapenv:Header>
<soapenv:Body>
<RetrieveRequestMsg xmlns="http://exacttarget.com/wsdl/partnerAPI">
<RetrieveRequest>
<ObjectType>Account</ObjectType>
<Properties>CustomerKey</Properties>
<Properties>Name</Properties>
<Properties>ID</Properties>
<Properties>EditionID</Properties>
<Properties>AccountType</Properties>
<Filter xsi:type="ns1:SimpleFilterPart" xmlns:ns1="http://exacttarget.com/wsdl/partnerAPI">
<Property>CustomerKey</Property>
<SimpleOperator>equals</SimpleOperator>
<Value>GM_DLEAR_123</Value>
</Filter>
<QueryAllAccounts>true</QueryAllAccounts>
</RetrieveRequest>
</RetrieveRequestMsg>
</soapenv:Body>
</soapenv:Envelope>
See Retrieving Account Object Using The CustomerKey Attribute for more information.