Both words are close synonyms:

Expectancy
The term has been applied to situations where an individual hopes and expects to receive something, generally property or money, but has no founded assurance of possession. A person named in a will as an heir has only an expectancy to inherit under the will, since there exists a possibility that the will may be altered so as to disinherit him or her.
expectancy
n. a possibility of future enjoyment of something one counts on receiving, usually referring to real property or the estate of a deceased person, such as a remainder, reversion, or distribution after the death of someone who has use for life
https://legal-dictionary.thefreedictionary.com/expectancy

A future interest held by one person in the real property of another that will take effect upon the expiration of the other property interests created at the same time as the future interest.
If Tom owns Blackacre in fee simple and conveys Blackacre to Bob for life and to Jane in fee simple, Jane has a vested remainder in fee that becomes a present interest upon the death of Bob. As a remainderman, she simply has to wait for Bob's death before assuming a present interest in Blackacre. (West's Encyclopedia of American Law)
:
2. Remainders are either vested or contingent. A vested remainder is one by which a present interest passes to the party. though to be enjoyed in future; and by which the estate is invariably fixed to remain to a determinate person, after the particular estate has been spent. Vide 2 Jo ins. R. 288; 1 Yeates, R. 340.
3. A contingent remainder is one which is limited to take effect on an event or condition, which may never happen or be performed, or which may not happen or be performed till after the determination of the preceding particular estate; in which case such remainder never can take effect. (A Law Dictionary)
https://legal-dictionary.thefreedictionary.com/Remainder

reversion an interest in an estate that reverts to the grantor or his heirs at the end of a period, such as at the end of the life of a grantee; or an estate so reverting. (Collins Dictionary of Law)
https://legal-dictionary.thefreedictionary.com/reversion

acquired rights and expectancies Pl. | die erworbenen Rechte und Anwartschaften
https://dict.leo.org/englisch-deutsch/expectancy

expectancy of pension ( SozV) = expectancy
expectancy / (SozV) Rentenanwartschaft
(Schäfer, Wirtschaftswörterbuch Englisch - Deutsch)

expectancy WIRTSCH JUR → Anwartschaft f
• estate in expectancy → Gut, auf das jemand Anwartschaft hat
• tables of expectancy in insurance → Mortalitäts-, Lebenserwartungstafeln
https://www.wordreference.com/ende/expectancy

remainder [JURA] | die Anwartschaft Pl.: die Anwartschaften - auf Grundbesitz [Sachenrecht]
remainder [JURA] | das Anwartschaftsrecht Pl. - auf Grundbesitz [Sachenrecht]
https://dict.leo.org/englisch-deutsch/remainder

The same applies for any potential remainders and claims for transfer of property including any potential ancillary rights and claims.
Gleiches gilt für eventuelle Anwartschaftsrechte und Eigentumsverschaffungsansprüche einschließlich eventueller Nebenrechte und -ansprüche.
https://context.reverso.net/übersetzung/deutsch-englisch/Anw...

vested right [JURA] | verbrieftes Recht
vested remainder [JURA] | unentziehbare Anwartschaft
https://dict.leo.org/englisch-deutsch/vested

contingent Adj. | bedingt
contingent (on) Adj. | abhängig (von)
contingently Adv. | eventuell [Abk.: evtl.]
https://dict.leo.org/englisch-deutsch/contingent

die sich gegenseitige überschneidenten Definitionen von vested/contigent remainder und expectancies kann man in Deutschen wie folgt zusammenfassen:

… und ob es sich um Besitz, Rückübertragung (Rückfall), bedingte oder verbriefte (unbedingte) Anwartschaften handelt