You raise some valuable points. I grew up speaking only Dutch at home, until we came to Australia when I was 8. I had to quickly learn to communicate in English. From then on, Dutch was the family language at home and English was spoken in all other situations. I was considered — and considered myself — bilingual.
As a consequence of this, I ended up at the end of my teens, speaking both languages ‘fluently’ — I could hold intelligent conversations in both — but there were areas in each where I lacked critical vocabulary. Because there were things I would talk about with friends — in English — that I would not discuss at home, I lacked the Dutch words and, as an adult, would struggle in a Dutch conversation on certain topics, such as personal relationships and sex. As there were also things that, as a child, I only discussed with my parents, my English vocabulary was lacking.
I also find that there is a difference — in my Dutch and other European languages I have learnt— in my ability to express myself and my ability to understand the written and/or spoken language. I can read Dutch ‘fluently’ — I resort to a dictionary no more than I would when reading English — but I need a dictionary close by when writing in Dutch.
One consequence, for me, of having a love for languages and linguistics, is that I have learned to speak a number of phrases in languages I don’t ‘speak’. with minimal ‘foreign’ accent. So, I can say in Russian, “Я не говорю по России” (I don’t speak Russian), and I am not believed.