Use SOAP API to retrieve email from Classic Tool:
<Envelope xmlns="http://schemas.xmlsoap.org/soap/envelope/" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<Header>
<fueloauth>YOUR_TOKEN_HERE</fueloauth>
</Header>
<Body>
<RetrieveRequestMsg xmlns="http://exacttarget.com/wsdl/partnerAPI">
<RetrieveRequest>
<ObjectType>Email</ObjectType>
<Properties>ID</Properties>
<Properties>Name</Properties>
<Properties>Subject</Properties>
<Properties>Status</Properties>
<Properties>PartnerKey</Properties>
<Properties>CreatedDate</Properties>
<Properties>Folder</Properties>
<Properties>CategoryID</Properties>
<Properties>EmailType</Properties>
<Properties>HTMLBody</Properties>
<Properties>ContentAreas</Properties>
<Filter xsi:type="SimpleFilterPart">
<Property>Id</Property>
<SimpleOperator>equals</SimpleOperator>
<Value>{EMAIL_ID_HERE}</Value>
</Filter>
</RetrieveRequest>
</RetrieveRequestMsg>
</Body>
Remove filter part to retrieve all emails or filter by CategoryId as @pkharries suggested
ID can be found in email properties.
Use REST API to retrieve email from Content Builder:
https://www.exacttargetapis.com/asset/v1/content/assets/{id}
GET /asset/v1/content/assets/{EMAIL_ID_HERE} HTTP/1.1
Host: www.exacttargetapis.com
Authorization: Bearer YOUR_TOKEN_HERE
Content-Type: application/json
Or retrieve all assets (filter by name for example):
GET /asset/v1/content/assets?$filter=Name%20like%20'Template'
HTTP/1.1
Host: www.exacttargetapis.com
Authorization: Bearer YOUR_TOKEN_HERE
Content-Type: application/json
ID can be found in email properties.