Yes, there is a significant difference, if we learn both English and other languages in the same English-speaking country like the US, Canada, or England. The basic idea is immersion, a preferred method of learning languages.
We know that generally a student will learn both English and another language in a classroom that is designed to learn that one language. Classrooms for learning most languages usually follow similar basic learning processes. One learns vocabulary and writing for either English or for Japanese, for example.
It could be that a student learns English or another language in an immersion class. An immersion class is one where native speakers of one language (Spanish, for example) learn in the same classroom more about their own language (Spanish) as well as the language of non-native speakers (English, for example) who are also in that class with the native speakers. Everyone in that immersion classroom is learning Spanish. But the fact that it is a classroom and not a whole culture where students learn a language remains the same.
The difference happens once the student needs to use the language, or to experience a whole culture in the real world. This is full cultural immersion outside the classroom. One draws upon what one has learned about a language new to them from their classroom learning. One must use that knowledge in a culture where that language is predominantly spoken. For example, as a native English speaker I already learned some Spanish in classrooms. I hope to become fluent, though. If I learn more Spanish here in the US, it will be much harder. Most people in this country do not speak Spanish, so I cannot become fluent easily.
I would however become fluent in Spanish much more quickly if I experienced complete immersion in a largely Spanish-speaking culture, except if perhaps I arranged somehow — and this would be hard to do — only to speak with people in a few neighborhoods in my mostly English-speaking city. That would be difficult to make happen in this mostly English-speaking culture. In order to experience language immersion in a whole culture, and in doing so learn much more effectively, I should live someplace where people mostly speak Spanish. If I lived for a year in Mexico City and had to speak, read, and write Spanish in order to get by — so that I could on my own travel, buy food, make friends, take classes, experience media, and so on — I would have to become immersed in the Spanish language.
We could apply this idea to a person from Singapore whose first language is not English. Suppose they are visiting San Francisco for a study or work year. She or he would quickly become immersed in an English-speaking culture. If the student took French at the same time, this cultural immersion could not happen for learning French. Like I would have for learning Spanish in the example above, while many people may speak French in San Francisco, English would be the much more widely spoken language. This means that the student would become much more fully immersed in English, not French. They would learn English much more readily here.
I hope this helps. Please me know if you have any questions.