If you want user edit gis data via internet, use Feature Server
If you don't want user edit gis data, read-only, use Map Server.
Feature Server would not export image, Map Server does.
Let's compare https://transparentgov.net/json2tree/esri/server/folder.html?url=https%3A%2F%2Fgis.cityofredlands.org%2Farcgis%2Frest%2Fservices&org=Redland+CA&_center_lat=40&_center_long=-74&_center_zoom=17&select_folder=204&select_layer=0
https://transparentgov.net/json2tree/esri/server/folder.html?url=https%3A%2F%2Fgis.cityofredlands.org%2Farcgis%2Frest%2Fservices&org=Redland+CA&_center_lat=40&_center_long=-74&_center_zoom=17&select_folder=34&select_layer=0
Map server example:
https://transparentgov.net:3200/googlemaps111/default?layer_id=0&layer=Trees¢er_lat=34.07867235222863¢er_long=-117.17836449579895¢er_zoom=17&url=https%3A%2F%2Fgis.cityofredlands.org%2Farcgis%2Frest%2Fservices%2FTreesOnly%2FMapServer&panto=0
Feature server example:
https://transparentgov.net:3200/googlemaps111/default?layer_id=0&layer=Trees¢er_lat=34.07869012495072¢er_long=-117.18024204210937¢er_zoom=17&url=https%3A%2F%2Fgis.cityofredlands.org%2Farcgis%2Frest%2Fservices%2FTreesOnly%2FFeatureServer&panto=0
https://community.esri.com/t5/arcgis-enterprise-questions/feature-service-vs-map-service/td-p/510166
https://gis.stackexchange.com/questions/126373/difference-between-feature-server-and-map-server
Unless, you need editing via REST API, then you need publish as a feature server.
How to enable feature server?
File Geodatabase or Enterprise Geodatabase registared with same Arcgis server is required, otherwise, you will run into error like this.
Warning: Both REST API are similar but not the same