As a native English speaker in England who was christened in the Church of England and is now Roman Catholic, I think the summary version is that all christenings involve baptism but not all baptisms are christenings.
Christening would refer to baptism in a church, typically in the presence of family and friends. It would most commonly be used in the Church of England and its derivative denominations.
It is possible for a baptism to take place outside of a church and/or to be conducted by a lay member and this would not typically be a “christening” I think?
It’s a bit odd that FamilySearch defaults to the terminology “christening” rather than “baptism” given this context.
Personally I don’t use the term christening as I am focused on ensuring consistency between all the denominations in my family - CofE, Church in Wales, Roman Catholic, Methodist, Baptist, Lutheran, and I’m sure there is something I have missed too.
Just my two pennies.