X escorts Y when X travels with Y and remains with Y the entire time, to ensure Y makes it to Y's destination. It can sometimes carry the implication Y is required to go where X wants under threat of force. It's unusual for this to be used where X and Y aren't a person or armored/military vehicles.
An escort can mean one who escorts someone as a service. It is also a euphemism for a (typically non-street level) prostitute especially if A) the one being escorted is male, B) the one doing the escorting is female, and C) the context is not any of military, jail/prison, protection, bodyguard, or personal/physical security. In these contexts you have nothing to worry about. But be particularly careful with the term "escort service".
X accompanies Y just means X will follow Y without the "make sure Y is safe/gets there OK" implication (or other implications) of escort. It's possible for X/Y here to be objects or services, and that general means if you obtain X, Y will be included with it, or that X and Y are part of an inseparable set or group.