Those are indeed different categories, with slightly different rights and requirements:
Salarié détaché/ICT only applies to people transferring internally within the same company/group. I don't see any immediate advantage for you as employee but it's useful for employers as they can use it to relocate people who wouldn't otherwise qualify (i.e. lower salary threshold). There is a simplified procedure for your family to come with you (no need to go through the regular regroupement familial process).
Passeport talent is a distinct category of visa/residence permits. This includes but is not limited to the “carte bleue européenne”. There is also a simplified procedure for your family to come with you (no need to go through the regular regroupement familial process). Since it doesn't require a pre-existing relationship with the (prospective) employer it applies to more people. The blue card corresponds to the “emploi hautement qualifié” sub-category of the “passeport talent” permit.
The blue card has steeper requirements than either the “salarié détaché” or “passeport talent salarié qualifié” permits but comes with distinct advantages, including building up a right to long-term stay in Europe. For you it would mean that it would be easier to change employers or even to move to another European country than if you were on salarié détaché/ICT permit.
You didn't mention it but note that there is also a regular salarié permit. There is no reason for you to be seeking this one but it might be useful to understand the logic of the system. The other permits (salarié détaché, passeport talent, carte bleue) have been created to offer easier paths to French residence (no autorisation de travail, no regroupement familial) for people who meet certain requirements (diploma, salary, working for an employer who has offices in France…) That's why there are many categories with slightly different rules. If you don't meet their requirements, you have to fall back to the salarié category, which is much less attractive (additionnal paperwork for the employer, your family has to wait before joining you, you need to have accommodation secured and prove it to get the permit/have your family join you).
Consequently, if your company is willing to go along with it and your lawyer thinks you would qualify, I see no downside to applying for a passeport talent, especially if it's a blue card. You should however check the requirements and rules carefully, I might be missing something. For your employer, the salarié détaché is an obvious choice, it should be slightly easier to get and reduces the risk you would leave them once you set foot in Europe.
In any case, you always need to ensure you satisfy all the requirements and have documents to prove it (including a work contract meeting the salary thresholds, diplomas, etc.) The list is not exactly the same for each of these permits.