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źródło definicji:
Wielki słownik polsko-angielski PWN-Oxford

agreement /e'griment/ n

1.(settlement, contract) ugoda f, porozumienie n (with sb/on sth z kimś/w sprawie czegoś);
an EU agreement- porozumienie w ramach Unii Europejskiej;
an Anglo-Irish agreement- porozumienie angielsko-irlandzkie;
an agreement to reduce nuclear arsenals- porozumienie w sprawie redukcji broni jądrowej;
to come to or reach an agreement- dojść do porozumienia, osiągnąć porozumienie;
hopes of an agreement- nadzieje na porozumienie;
under an agreement- na mocy porozumienia or ugody
2. (undertaking) zobowiązanie n (to do sth do czegoś, do zrobienia czegoś);
an agreement to repay the loan- zobowiązanie do spłacenia pożyczki;
3. (mutual understanding) zgoda f (about or on sth co do czegoś); porozumienie n (about or on sth w sprawie czegoś); to be in agreement with sb- zgadzać się z kimś;
by agreement with sb- w porozumieniu z kimś;
to reach agreement -dojść do porozumienia or zgody;
4. Jur (contract) umowa f; under the terms of the agreement -na mocy umowy, zgodnie z warunkami umowy
5. (consent) zgoda f, przyzwolenie n (to sth na coś) [reform, cease-fire, moratorium]
6. Ling związek m zgody
settlement /'setlment/ n

1. (agreement) porozumienie, ugoda
2. (resolving) rozwiązywanie n; settlement of industrial disputes- rozwiązywanie sporów pracowniczych
3. Jur (in civil case) ugoda f; (of property) zapisanie n;
a marriage settlement- majątkowa umowa małżeńska;
to make a settlement on sb -zrobić zapis na rzecz kogoś
4. Fin (of debt) spłacenie n; (of bill) uregulowanie n; (of invoice, claim) rozliczenie n;
prompt settlement of your account would be appreciated- bylibyśmy wdzięczni za rychłe uzupełnienie konta;
in settlement of sth- na pokrycie czegoś, w rozliczeniu czegoś [cheque]

Pozdrawiam

Najprościej:
Używaj 'agreement' w sensie: umowa, porozumienie - kiedy dwie strony podejmują jakieś decyzje dotyczące przyszłości, np. "sign an agreement" (podpisać umowę), "come to an agreement" (dojść do porozumienia), "reach an agreement" (osiągnąć porozumienie)
'settlement' w sensie: ugoda, rozstrzygniecie sporu - kiedy jest jakiś konflikt, np.: 'reach a settlement' (zawrzeć ugodę), 'out-of-court settlement' (ugoda polubowna)
'arrangement' w sensie: plany, ustalenia, przygotowania - kiedy ktoś lub więcej osób ustala jak coś ma się odbywać, np.: "make arrangements' (poczynić plany, umówić się), 'have an arrangement with sb' (ustalić coś z kimś)
'Agreement' może być formalną umową, ustną lub pisemną, 'arrangements' to ustalenia, najczęściej tymczasowe. 'Agreement' jako 'porozumienie' sugeruje, że nie było wcześniej wspólnego stanowiska, 'settlement' natomiast, że był konflikt między stronami.
"It looks like a compromise agreement has been reached."
"She accepted an out-of-court settlement of $4,000."
"The cave can only be visited by prior arrangement."

Następne zestawienie [1]:

settle‧ment

COLLOCATIONS

verbs
reach a settlement The companies reached a settlement in March.
achieve a settlement (= after a lot of discussions )
The government was determined to achieve a settlement in Northern Ireland.
negotiate a settlement (= have discussions to try to reach a settlement )
His lawyers are understood to be negotiating a settlement.
ADJECTIVES/NOUN + settlement
an amicable settlement (= when people agree in a friendly way ) Disputes were often taken to a village council, which attempted to bring about an amicable settlement.
a peaceful settlement (= without fighting ) Both sides are working towards a peaceful settlement.
a political settlement (= one that is reached by political discussion, not fighting )
The British government favours a political settlement in the Middle East.
a peace settlement (= one which ends a war ) Hopes of a peace settlement receded.
a divorce settlement (= an agreement about money and property at the end of a marriage )
She acquired full ownership of the building in her 1986 divorce settlement.
an out-of-court settlement (= an agreement made to avoid a court case )


agreement

COLLOCATIONS
verbs
make an agreement We made an agreement not to tell anyone.
sign an agreement The two countries have signed an agreement on military co-operation.
break/violate an agreement The UN accused the country's leaders of breaking international agreements.
be bound by an agreement (= have to obey the conditions of an official agreement )
India is bound by the agreements signed under the World Trade Organisation.

ADJECTIVES/NOUN + agreement
a written agreement There is usually a written agreement between the borrower and the bank.
a verbal agreement (= agreed in words, but not written down ) The doctor needs to have a verbal agreement from the patient.
a peace agreement (= a permanent agreement to stop fighting )
The five countries in the region signed a peace agreement.
a ceasefire agreement (= a temporary agreement to stop fighting )

phrases
the terms of an agreement (= the conditions that people agree on )
Under the terms of the agreement, the debt would be repaid over a 20-year period.
a breach of an agreement (= an act of breaking an agreement )


źródło:
1.Longman Dictionary of Contemporary English 5th Edition New Edition