From my understanding Colonialism is direct of control over a land mass and resources that suppresses its indigenous population where Imperialism is an economic and military subjugation of a indigenous government who use their population to extract wealth to give the empire.

Rome did both. Their actions on the british isles and Gaul were more colonial because they had tribal political systems. In Egypt and Greece they were more Imperial because they had more developed government systems.

yeah, they established colonies to extract surplus value from the people living there. you can go even further to describe their conquest as settler-colonialism, as Roman citizens migrated into many of these colonies and enjoyed a privileged position over the people they colonized. this “colonialism” was more of a tributary relationship tho, as taxation was very localized and it was likely that these colonies had more autonomy than what we think when we talk abt colonialism. ur right that it was proto-imperialism since “imperialism” in the way we use it is in the context of capitalism. imperialism requires monopolies, finance capital dominance, and a unified international capital on top of colonization. ig the reasoning for it being proto-imperialism is that the colonization was spread through an entire continent, capital was being formed (Rome had a sort of proto-capitalism), and land ownership was highly concentrated

Its hard to estimate but suposedly occitan spanish and italian are more similar to each other than either is to french because there was more italian migration to colonies in the western mediterranean. So there probably was roman colonialism in southern france and spain but even then it probably was limited.

Edit. I checked and aparently i was wrong. so from table 7.3 in the demografics of roman italy(not really a good book but its on hand and the original brunt article is not) there semed to have been between 375k and 500k adult roman citizens living outside italy in 28 ce. These are mostly colonists. For comparison 188k spanish migramts to the new world between 1580 -1640 158k 1640-1700 and 193k 1700-1760. From england this was 293k 248k 372k.(this taken from "the colonial origins of the divergence in the americas a labor market aproach" allen et al 2012) Given that the roman 500k is a snapshot it should be more or less comparable to the 60 year periods above. In a much smaller area. This is probably compensated by the native americans having much lower population densities because of the eurasian plages. So aparently roman colonialism into spain and southern france was similar demografically to spanish colonialism in the americas. Honestly i was not expecting that.